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+[
+  {
+    "title": "What is the probability that a random symmetric tensor is close to   rank-one?",
+    "authors": [
+      "Alberto Cazzaniga",
+      "Antonio Lerario",
+      "Andrea Rosana"
+    ],
+    "abstract": "We address the general problem of estimating the probability that a real symmetric tensor is close to rank-one tensors. Using Weyl's tube formula, we turn this question into a differential geometric one involving the study of metric invariants of the real Veronese variety. More precisely, we give an explicit formula for its reach and curvature coefficients with respect to the Bombieri-Weyl metric. These results are obtained using techniques from Random Matrix theory and an explicit description of the second fundamental form of the Veronese variety in terms of GOE matrices. Our findings give a complete solution to the original problem. In the case of rational normal curves it leads to a simple formula describing explicitly exponential decay with respect to the degree of the tensor.",
+    "arxiv_id": "2301.05502v3",
+    "categories": [
+      "math.AG",
+      "math.DG",
+      "math.PR"
+    ],
+    "primary_category": "math.AG",
+    "published_date": "2023-01-13T12:07:42Z",
+    "updated_date": "2024-12-09T16:30:32Z",
+    "pdf_url": "https://arxiv.org/pdf/2301.05502v3",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2301.05502v3.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "A Hodge Theory for Entanglement Cohomology",
+    "authors": [
+      "Christian Ferko",
+      "Eashan Iyer",
+      "Kasra Mossayebi",
+      "Gregor Sanfey"
+    ],
+    "abstract": "We explore and extend the application of homological algebra to describe quantum entanglement, initiated in arXiv:1901.02011, focusing on the Hodge-theoretic structure of entanglement cohomology in finite-dimensional quantum systems. We construct analogues of the Hodge star operator, inner product, codifferential, and Laplacian for entanglement $k$-forms. We also prove that such $k$-forms obey versions of the Hodge isomorphism theorem and Hodge decomposition, and that they exhibit Hodge duality. As a corollary, we conclude that the dimensions of the $k$-th and $(n-k)$-th cohomologies coincide for entanglement in $n$-partite pure states, which explains a symmetry property (\"Poincare duality\") of the associated Poincare polynomials.",
+    "arxiv_id": "2410.12529v2",
+    "categories": [
+      "hep-th",
+      "math-ph",
+      "math.AT",
+      "math.MP",
+      "quant-ph"
+    ],
+    "primary_category": "hep-th",
+    "published_date": "2024-10-16T13:09:56Z",
+    "updated_date": "2024-12-03T03:14:20Z",
+    "pdf_url": "https://arxiv.org/pdf/2410.12529v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2410.12529v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Constructing Multipartite Planar Maximally Entangled States from Phase   States and Quantum Secret Sharing Protocol",
+    "authors": [
+      "Lahoucine Bouhouch",
+      "Yassine Dakir",
+      "Abdallah Slaoui",
+      "Rachid Ahl Laamara"
+    ],
+    "abstract": "In this paper, we explore the construction of Planar Maximally Entangled (PME) states from phase states. PME states form a class of $n$-partite states in which any subset of adjacent particles whose size is less than or equal to half the total number of particles is in a fully entangled state. This property is essential to ensuring the robustness and stability of PME states in various quantum information applications. We introduce phase states for a set of so-called noninteracting $n$ particles and describe their corresponding separable density matrices. These phase states, although individually separable, serve as a starting point for the generation of entangled states when subjected to unitary dynamics. Using this method, we suggest a way to make complex multi-qubit states by watching how unconnected phase states change over time with a certain unitary interaction operator. In addition, we show how to derive PME states from these intricate phase states for two-, three-, four-, and K-qubit systems. This method of constructing PME states is particularly relevant for applications in fields such as quantum teleportation, quantum secret sharing, and quantum error correction, where multiparty entanglement plays a central role in the efficiency of the protocols.",
+    "arxiv_id": "2411.15077v1",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2024-11-22T17:10:58Z",
+    "updated_date": "2024-11-22T17:10:58Z",
+    "pdf_url": "https://arxiv.org/pdf/2411.15077v1",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2411.15077v1.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Casimir effect of a rough membrane in an Aether-like Lorentz-violating   scenario",
+    "authors": [
+      "Byron Droguett",
+      "Claudio B\u00f3rquez"
+    ],
+    "abstract": "We explore the Casimir effect of a rough membrane within the framework of theories that break Lorentz symmetry. We consider two constant Aether vectors: one timelike and other spacelike, simultaneously. We employ an appropriate change of coordinates such that the membrane assumes a completely flat border and the remaining terms associated with the roughness are considered as part of the potential. Quantum fluctuations are induced by a scalar quantum field subject to Dirichlet boundary conditions. The spectrum is obtained through perturbation theory and regularized using the $\\zeta$--function method. We provide an explicit example of a membrane with periodic boundaries. The presence of Aether vectors has a significant impact on the dominant term of the Casimir effect, while roughness only affects the secondary terms. Additionally, we examine the finite-temperature case.",
+    "arxiv_id": "2404.13187v3",
+    "categories": [
+      "hep-th",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "hep-th",
+    "published_date": "2024-04-19T21:23:10Z",
+    "updated_date": "2024-11-18T18:33:38Z",
+    "pdf_url": "https://arxiv.org/pdf/2404.13187v3",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2404.13187v3.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Resources of the Quantum World",
+    "authors": [
+      "Gilad Gour"
+    ],
+    "abstract": "This book delves into the burgeoning field of quantum resource theories, a novel and vibrant area of research within quantum information science that seeks to unify diverse quantum phenomena under a single framework. By recognizing various attributes of physical systems as \"resources,\" this approach offers a fresh perspective on quantum phenomena, transforming our understanding and application of concepts such as quantum entanglement, coherence, and more. With a focus on the pedagogical, the book aims to equip readers with the advanced mathematical tools and physical principles needed to navigate and contribute to this rapidly evolving field. It covers a wide range of topics, from the foundational aspects of quantum mechanics and quantum information to detailed explorations of specific resource theories, including entanglement, asymmetry, and thermodynamics. Through rigorous mathematical exposition and a unique axiomatic approach, the book provides deep insights into the operational and conceptual frameworks that underpin quantum resource theories, making it an invaluable resource for graduate students, early-career researchers, and anyone interested in the cutting-edge developments in quantum information science.",
+    "arxiv_id": "2402.05474v2",
+    "categories": [
+      "quant-ph",
+      "cs.IT",
+      "math-ph",
+      "math.IT",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2024-02-08T08:05:02Z",
+    "updated_date": "2024-11-18T10:03:41Z",
+    "pdf_url": "https://arxiv.org/pdf/2402.05474v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2402.05474v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Quantum entanglement as an ambiguity of classical dynamics",
+    "authors": [
+      "Piotr Dulian",
+      "Adam Sawicki"
+    ],
+    "abstract": "We study consequences of applying formalism of symplectic geometry to quantum mechanics. We propose a physical interpretation of a symplectic indicator of entanglement, introduced in [1], given by the degeneracy of the symplectic form on manifolds of locally unitary equivalent states. We show that this degeneracy can be understood as an ambiguity of some classical dynamic.",
+    "arxiv_id": "2410.21949v1",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2024-10-29T11:07:48Z",
+    "updated_date": "2024-10-29T11:07:48Z",
+    "pdf_url": "https://arxiv.org/pdf/2410.21949v1",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2410.21949v1.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Fermionic Casimir Energy in Horava-Lifshitz Scenario",
+    "authors": [
+      "E. R. Bezerra de Mello",
+      "M. B. Cruz"
+    ],
+    "abstract": "In this work, we investigate the violation of Lorentz symmetry through the Casimir effect. The Casimir effect is one of the most intriguing aspects of modern physics, representing a macroscopic quantum-origin force between two neutral conducting surfaces, and it stands as a triumph of Quantum Field Theory. Here, we examine the Casimir effects associated with a massive fermionic quantum field confined in the region between two large and parallel plates within the Horava-Lifshitz framework of Lorentz symmetry violation. To calculate the Casimir energy and consequently the Casimir pressure, we impose a MIT bag boundary condition on two plates, compatible with the higher-order derivative term in the modified Dirac equation. Our results indicate a strong influence of Lorentz violation on the Casimir effect. We observe that the Casimir energy is affected, both in intensity and sign, potentially exhibiting repulsive or attractive force between the plates, depending on the critical exponent associated with the Horava-Lifshitz formalism.",
+    "arxiv_id": "2407.11749v2",
+    "categories": [
+      "hep-th",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "hep-th",
+    "published_date": "2024-07-16T14:16:06Z",
+    "updated_date": "2024-10-28T16:54:43Z",
+    "pdf_url": "https://arxiv.org/pdf/2407.11749v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2407.11749v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Entanglement in Algebraic Quantum Field Theories",
+    "authors": [
+      "Rafael Grossi"
+    ],
+    "abstract": "There has been some recent interest in applying the techniques of Algebraic Quantum Field Theory (AQFT) to entanglement problems in perturbative QFT. In particular, the Hilbert space independence of this formulation makes it particularly interesting in the context of curved spacetimes and the emphasis on the algebra of observables makes the treatment of Bell inequalities in QFT resemble such treatment in non-relativistic Quantum Mechanics. In this work, we present the mathematical structures needed for formulating AQFT in terms of the Haag-Araki-Kastler (HAK) axioms and discuss their implications. Moreover, we discuss the algebraic approach to quantum entanglement in the form of Bell inequalities. We provide an extension of this formulation to general globally hyperbolic spacetimes using the so-called Locally Covariant approach to QFT, which extends the HAK axioms to general spacetimes by means of the Category Theory language.",
+    "arxiv_id": "2410.16599v1",
+    "categories": [
+      "math-ph",
+      "math.MP",
+      "quant-ph"
+    ],
+    "primary_category": "math-ph",
+    "published_date": "2024-10-22T00:53:30Z",
+    "updated_date": "2024-10-22T00:53:30Z",
+    "pdf_url": "https://arxiv.org/pdf/2410.16599v1",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2410.16599v1.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Quantum teleportation implies symmetry-protected topological order",
+    "authors": [
+      "Yifan Hong",
+      "David T. Stephen",
+      "Aaron J. Friedman"
+    ],
+    "abstract": "We constrain a broad class of teleportation protocols using insights from locality. In the \"standard\" teleportation protocols we consider, all outcome-dependent unitaries are Pauli operators conditioned on linear functions of the measurement outcomes. We find that all such protocols involve preparing a \"resource state\" exhibiting symmetry-protected topological (SPT) order with Abelian protecting symmetry $\\mathcal{G}_{k}= (\\mathbb{Z}_2 \\times \\mathbb{Z}_2)^k$. The $k$ logical states are teleported between the edges of the chain by measuring the corresponding $2k$ string order parameters in the bulk and applying outcome-dependent Paulis. Hence, this single class of nontrivial SPT states is both necessary and sufficient for the standard teleportation of $k$ qubits. We illustrate this result with several examples, including the cluster state, variants thereof, and a nonstabilizer hypergraph state.",
+    "arxiv_id": "2310.12227v4",
+    "categories": [
+      "quant-ph",
+      "cond-mat.str-el",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2023-10-18T18:02:23Z",
+    "updated_date": "2024-10-10T15:59:30Z",
+    "pdf_url": "https://arxiv.org/pdf/2310.12227v4",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2310.12227v4.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Quantum Entanglement on Black Hole Horizons in String Theory and   Holography",
+    "authors": [
+      "Atish Dabholkar",
+      "Upamanyu Moitra"
+    ],
+    "abstract": "We compute the exact one-loop partition function of $\\mathbb{Z}_N$ orbifolds of Euclidean BTZ black hole with the aim to compute the entanglement entropy of the black hole horizon in string theory as a function of the mass and spin of the black hole and the $\\mathrm{AdS}_3$ radius. We analyze the tachyonic contribution to the modular integrand for the partition function known for odd integers $N>1$ and show that it admits an analytic continuation resulting in a finite answer for the modular integral in the physical region $0< N \\leq 1$. We discuss the flat space limit and the relevance of this computation for quantum gravity near black hole horizons and holography in relation to the thermal entropy.",
+    "arxiv_id": "2312.14253v2",
+    "categories": [
+      "hep-th",
+      "gr-qc",
+      "math-ph",
+      "math.MP",
+      "quant-ph"
+    ],
+    "primary_category": "hep-th",
+    "published_date": "2023-12-21T19:11:57Z",
+    "updated_date": "2024-09-24T12:47:08Z",
+    "pdf_url": "https://arxiv.org/pdf/2312.14253v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2312.14253v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Finite Entanglement Entropy in String Theory",
+    "authors": [
+      "Atish Dabholkar",
+      "Upamanyu Moitra"
+    ],
+    "abstract": "We analyze the one-loop quantum entanglement entropy in ten-dimensional Type-II string theory using the orbifold method by analytically continuing in $N$ the genus-one partition function for string orbifolds on $\\mathbb{R}^2/\\mathbb{Z}_N$ conical spaces known for all odd integers $N > 1$. We show that the tachyonic contributions to the orbifold partition function can be appropriately summed and analytically continued to an expression that is finite in the physical region $0 < N \\leq 1$ resulting in a finite and calculable answer for the entanglement entropy. We discuss the implications of the finiteness of the entanglement entropy for the information paradox, quantum gravity, and holography.",
+    "arxiv_id": "2306.00990v2",
+    "categories": [
+      "hep-th",
+      "gr-qc",
+      "math-ph",
+      "math.MP",
+      "quant-ph"
+    ],
+    "primary_category": "hep-th",
+    "published_date": "2023-06-01T17:59:59Z",
+    "updated_date": "2024-09-24T12:09:25Z",
+    "pdf_url": "https://arxiv.org/pdf/2306.00990v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2306.00990v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "The Stochastic Casimir Effect",
+    "authors": [
+      "Ruibo Kou",
+      "Roger Tribe",
+      "Oleg Zaboronski"
+    ],
+    "abstract": "We model the one-dimensional `classical' vacuum by a system of annihilating Brownian motions on $\\mathbb{R}$ with pairwise immigration. A pair of reflecting or absorbing walls placed in such a vacuum at separation $L$ experiences an attractive force which decays exponentially with $L$. This phenomenon can be regarded as a purely classical Casimir effect for a system of interacting Brownian motions.",
+    "arxiv_id": "2409.15222v1",
+    "categories": [
+      "math.PR",
+      "math-ph",
+      "math.MP",
+      "82C22, 81T55"
+    ],
+    "primary_category": "math.PR",
+    "published_date": "2024-09-23T17:10:37Z",
+    "updated_date": "2024-09-23T17:10:37Z",
+    "pdf_url": "https://arxiv.org/pdf/2409.15222v1",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2409.15222v1.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Entanglement cost of realizing quantum processes",
+    "authors": [
+      "Xin Wang",
+      "Mingrui Jing",
+      "Chengkai Zhu"
+    ],
+    "abstract": "Quantum entanglement, a peculiar connection between particles, underpins powerful technologies such as quantum computing and secure communication. However, quantifying the minimum entanglement required to prepare quantum states and implement quantum processes remains a significant challenge. We develop an efficiently computable tool that reliably estimates the amount of entanglement needed for realizing arbitrary quantum processes respecting certain physical principles. Our tool applies to the entanglement required to prepare a broad range of quantum states in the asymptotic regime, surpassing previous methods' limitations. We also confirm that entanglement, once consumed to realize the considered class of quantum operations, cannot be fully recovered, even asymptotically. This irreversible behavior is evident for full-rank entangled states and practically relevant amplitude damping channels, even under quantum operations that completely preserve the positivity of partial transpose. We showcase our approach's power through examples such as estimating entanglement requirements for realizing bipartite dephasing SWAP channels and solving Hamiltonian simulations under thermal interaction, highlighting its advantages over existing techniques. Our work provides a practical toolkit for benchmarking entanglement requirements for generic states and quantum dynamics, paving the way for assessing and optimizing the performances of quantum technologies.",
+    "arxiv_id": "2311.10649v2",
+    "categories": [
+      "quant-ph",
+      "cond-mat.str-el",
+      "cs.IT",
+      "hep-th",
+      "math-ph",
+      "math.IT",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2023-11-17T17:07:26Z",
+    "updated_date": "2024-09-22T16:19:47Z",
+    "pdf_url": "https://arxiv.org/pdf/2311.10649v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2311.10649v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Asymptotic quantification of entanglement with a single copy",
+    "authors": [
+      "Ludovico Lami",
+      "Mario Berta",
+      "Bartosz Regula"
+    ],
+    "abstract": "Despite the central importance of quantum entanglement in fueling many quantum technologies, the understanding of the optimal ways to exploit it is still beyond our reach, and even measuring entanglement in an operationally meaningful way is prohibitively difficult. This is due to the need to precisely characterise many-copy, asymptotic protocols for entanglement processing. Here we overcome these issues by introducing a new way of benchmarking the fundamental protocol of entanglement distillation (purification), where instead of measuring its asymptotic yield, we focus on the best achievable error. We connect this formulation of the task with an information-theoretic problem in composite quantum hypothesis testing known as generalised Sanov's theorem. By solving the latter problem -- which had no previously known solution even in classical information theory -- we thus compute the optimal asymptotic error exponent of entanglement distillation. We show this asymptotic solution to be given by the reverse relative entropy of entanglement, a single-letter quantity that can be evaluated using only a single copy of a quantum state, which is a unique feature among operational measures of entanglement. Altogether, we thus demonstrate a measure of entanglement that admits a direct operational interpretation as the optimal asymptotic rate of an important entanglement manipulation protocol while enjoying an exact, single-letter formula.",
+    "arxiv_id": "2408.07067v2",
+    "categories": [
+      "quant-ph",
+      "cs.IT",
+      "math-ph",
+      "math.IT",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2024-08-13T17:57:59Z",
+    "updated_date": "2024-09-19T13:29:05Z",
+    "pdf_url": "https://arxiv.org/pdf/2408.07067v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2408.07067v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Edge modes, extended TQFT, and measurement based quantum computation",
+    "authors": [
+      "Gabriel Wong"
+    ],
+    "abstract": "Quantum teleportation can be used to define a notion of parallel transport which characterizes the entanglement structure of a quantum state \\cite{Czech:2018kvg}. This suggests one can formulate a gauge theory of entanglement. In \\cite{Wong:2022mnv}, it was explained that measurement based quantum computation in one dimension can be understood in term of such a gauge theory (MBQC). In this work, we give an alternative formulation of this \"entanglement gauge theory\" as an extended topological field theory. This formulation gives a alternative perspective on the relation between the circuit model and MBQC. In addition, it provides an interpretation of MBQC in terms of the extended Hilbert space construction in gauge theories, in which the entanglement edge modes play the role of the logical qubit.",
+    "arxiv_id": "2312.00605v3",
+    "categories": [
+      "hep-th",
+      "cond-mat.other",
+      "math-ph",
+      "math.MP",
+      "quant-ph"
+    ],
+    "primary_category": "hep-th",
+    "published_date": "2023-12-01T14:11:31Z",
+    "updated_date": "2024-09-11T13:18:42Z",
+    "pdf_url": "https://arxiv.org/pdf/2312.00605v3",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2312.00605v3.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Multipartite entanglement",
+    "authors": [
+      "Pawel Horodecki",
+      "\u0141ukasz Rudnicki",
+      "Karol \u017byczkowski"
+    ],
+    "abstract": "In this contribution we present a concise introduction to quantum entanglement in multipartite systems. After a brief comparison between bipartite systems and the simplest non-trivial multipartite scenario involving three parties, we review mathematically rigorous definitions of separability and entanglement between several subsystems, as well as their transformations and measures.",
+    "arxiv_id": "2409.04566v1",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2024-09-06T19:05:15Z",
+    "updated_date": "2024-09-06T19:05:15Z",
+    "pdf_url": "https://arxiv.org/pdf/2409.04566v1",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2409.04566v1.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "A Review of Stable, Traversable Wormholes in f (R) Gravity Theories",
+    "authors": [
+      "Ramesh Radhakrishnan",
+      "Patrick Brown",
+      "Jacob Mutulevich",
+      "Eric Davis",
+      "Delaram Mirfendereski",
+      "Gerald Cleaver"
+    ],
+    "abstract": "It has been proven that in standard Einstein gravity, exotic matter is required to stabilize traversable wormholes. Quantum field theory permits these violations due to the quantum coherent effects found in any quantum field. Even reasonable classical scalar fields violate the energy conditions. In the case of the Casimir effect and squeezed vacuum states, these violations have been experimentally proven. It is advantageous to investigate methods to minimize the use of exotic matter. One such area of interest is extended theories of Einstein gravity. It has been claimed that in some extended theories, stable traversable wormholes solutions can be found without the use of exotic matter. There are many extended theories of gravity, and in this review paper, we first explore modified gravity theories and then explore some wormhole solutions in such theories, including Lovelock gravity and Einstein Dilaton Gauss Bonnet gravity. For completeness, we have also reviewed other wormholes such as Casimir wormholes, dark matter halo wormholes, thin-shell wormholes, and Nonlocal Gravity wormholes, where alternative techniques are used to either avoid or reduce the amount of exotic matter that is required.",
+    "arxiv_id": "2405.05476v2",
+    "categories": [
+      "gr-qc",
+      "hep-th",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "gr-qc",
+    "published_date": "2024-05-09T00:26:37Z",
+    "updated_date": "2024-09-04T18:53:37Z",
+    "pdf_url": "https://arxiv.org/pdf/2405.05476v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2405.05476v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Complementarity between quantum entanglement, geometrical and dynamical   appearances in N spin-$1/2$ system under all-range Ising model",
+    "authors": [
+      "Jamal Elfakir",
+      "Brahim Amghar",
+      "Abdallah Slaoui",
+      "Mohammed Daoud"
+    ],
+    "abstract": "With the growth of geometric science, including the methods of exploring the world of information by means of modern geometry, there has always been a mysterious and fascinating ambiguous link between geometric, topological and dynamical characteristics with quantum entanglement. Since geometry studies the interrelations between elements such as distance and curvature, it provides the information sciences with powerful structures that yield practically useful and understandable descriptions of integrable quantum systems. We explore here these structures in a physical system of $N$ interaction spin-$1/2$ under all-range Ising model. By performing the system dynamics, we determine the Fubini-Study metric defining the relevant quantum state space. Applying Gaussian curvature within the scope of the Gauss-Bonnet theorem, we proved that the dynamics happens on a closed two-dimensional manifold having both a dumbbell-shape structure and a spherical topology. The geometric and topological phases appearing during the system evolution processes are sufficiently discussed. Subsequently, we resolve the quantum brachistochrone problem by achieving the time-optimal evolution. By restricting the whole system to a two spin-$1/2$ system, we investigate the relevant entanglement from two viewpoints; The first is of geometric nature and explores how the entanglement level affects derived geometric structures such as the Fubini-Study metric, the Gaussian curvature, and the geometric phase. The second is of dynamic nature and addresses the entanglement effect on the evolution speed and the related Fubini-Study distance. Further, depending on the degree of entanglement, we resolve the quantum brachistochrone problem.",
+    "arxiv_id": "2304.05278v3",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2023-04-11T15:26:19Z",
+    "updated_date": "2024-08-30T20:43:28Z",
+    "pdf_url": "https://arxiv.org/pdf/2304.05278v3",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2304.05278v3.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "The Yang-Baxter equation, Quantum computing and Quantum entanglement",
+    "authors": [
+      "Fabienne Chouraqui"
+    ],
+    "abstract": "We present a method to construct infinite families of entangling $2$-qudit gates, and amongst them entangling $2$-qudit gates which satisfy the Yang-Baxter equation. We show that, given $2$-qudit gates $c$ and $d$, if $c$ or $d$ is entangling, then their Tracy-Singh product $c \\boxtimes d$ is also entangling and we can provide non-entangled states which become entangled after the application of $c \\boxtimes d$.",
+    "arxiv_id": "2303.02964v4",
+    "categories": [
+      "math.GR",
+      "math-ph",
+      "math.MP",
+      "math.QA"
+    ],
+    "primary_category": "math.GR",
+    "published_date": "2023-03-06T08:48:50Z",
+    "updated_date": "2024-08-25T08:11:25Z",
+    "pdf_url": "https://arxiv.org/pdf/2303.02964v4",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2303.02964v4.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Classifying Entanglement by Algebraic Geometry",
+    "authors": [
+      "Masoud Gharahi"
+    ],
+    "abstract": "Quantum Entanglement is one of the key manifestations of quantum mechanics that separate the quantum realm from the classical one. Characterization of entanglement as a physical resource for quantum technology became of uppermost importance. While the entanglement of bipartite systems is already well understood, the ultimate goal to cope with the properties of entanglement of multipartite systems is still far from being realized. This dissertation covers characterization of multipartite entanglement using algebraic-geometric tools. Firstly, we establish an algorithm to classify multipartite entanglement by $k$-secant varieties of the Segre variety and $\\ell$-multilinear ranks that are invariant under Stochastic Local Operations with Classical Communication (SLOCC). We present a fine-structure classification of multiqubit and tripartite entanglement based on this algorithm. Another fundamental problem in quantum information theory is entanglement transformation that is quite challenging regarding to multipartite systems. It is captivating that the proposed entanglement classification by algebraic geometry can be considered as a reference to study SLOCC and asymptotic SLOCC interconversions among different resources based on tensor rank and border rank, respectively. In this regard, we also introduce a new class of tensors that we call \\emph{persistent tensors} and construct a lower bound for their tensor rank. We further cover SLOCC convertibility of multipartite systems considering several families of persistent tensors.",
+    "arxiv_id": "2408.12265v1",
+    "categories": [
+      "quant-ph",
+      "cs.CC",
+      "math-ph",
+      "math.AG",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2024-08-22T10:03:22Z",
+    "updated_date": "2024-08-22T10:03:22Z",
+    "pdf_url": "https://arxiv.org/pdf/2408.12265v1",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2408.12265v1.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Generating quantum dissonance via local operations",
+    "authors": [
+      "G\u00f6khan Torun"
+    ],
+    "abstract": "Correlations may arise in quantum systems through various means, of which the most remarkable one is quantum entanglement. Additionally, there are systems that exhibit non-classical correlations even in the absence of entanglement. Quantum dissonance refers to how quantum discord (QD) -- the difference between the total correlation and the classical correlation in a given quantum state -- appears as a non-classical correlation in a system without entanglement. It could be said that QD has the potential to provide a more inclusive viewpoint for discerning the non-classical correlations. In this work, we address the problem of manipulating the QD between two subsystems through local operations. We propose two explicit procedures for obtaining separable Werner states, a type of mixed state with nonzero QD. Both approaches involve performing local operations on classically correlated states and offers a step-by-step method for obtaining separable Werner states with nonzero discord, providing an alternative (explicit and user-friendly) to existing methods.",
+    "arxiv_id": "2405.08568v2",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2024-05-14T13:02:05Z",
+    "updated_date": "2024-08-12T10:52:09Z",
+    "pdf_url": "https://arxiv.org/pdf/2405.08568v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2405.08568v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Penrose dodecahedron, Witting configuration and quantum entanglement",
+    "authors": [
+      "Alexander Yu. Vlasov"
+    ],
+    "abstract": "A model with two entangled spin-3/2 particles based on geometry of dodecahedron was suggested by Roger Penrose for formulation of analogue of Bell theorem \"without probabilities.\" The model was later reformulated using so-called Witting configuration with 40 rays in 4D Hilbert space. However, such reformulation needs for some subtleties related with entanglement of two such configurations essential for consideration of non-locality and some other questions. Two entangled systems with quantum states described by Witting configurations are discussed in presented work. Duplication of points with respect to vertices of dodecahedron produces rather significant increase with number of symmetries in 25920/60=432 times. Quantum circuits model is a natural language for description of operations with different states and measurements of such systems.",
+    "arxiv_id": "2208.13644v2",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2022-08-29T14:46:44Z",
+    "updated_date": "2024-08-07T09:23:35Z",
+    "pdf_url": "https://arxiv.org/pdf/2208.13644v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2208.13644v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Estimate distillable entanglement and quantum capacity by squeezing   useless entanglement",
+    "authors": [
+      "Chengkai Zhu",
+      "Chenghong Zhu",
+      "Xin Wang"
+    ],
+    "abstract": "Quantum Internet relies on quantum entanglement as a fundamental resource for secure and efficient quantum communication, reshaping data transmission. In this context, entanglement distillation emerges as a crucial process that plays a pivotal role in realizing the full potential of the quantum internet. Nevertheless, it remains challenging to accurately estimate the distillable entanglement and its closely related essential quantity, the quantum capacity. In this work, we consider a general resource measure known as the reverse divergence of resources which quantifies the minimum divergence between a target state and the set of free states. Leveraging this measure, we propose efficiently computable upper bounds for both quantities based on the idea that the useless entanglement within a state or a quantum channel does not contribute to the distillable entanglement or the quantum capacity, respectively. Our bounds can be computed via semidefinite programming and have practical applications for purifying maximally entangled states under practical noises, such as depolarizing and amplitude damping noises, leading to improvements in estimating the one-way distillable entanglement. Furthermore, we provide valuable benchmarks for evaluating the quantum capacities of qubit quantum channels, including the Pauli channels and the random mixed unitary channels, which are of great interest for the development of a quantum internet.",
+    "arxiv_id": "2303.07228v4",
+    "categories": [
+      "quant-ph",
+      "cs.IT",
+      "math-ph",
+      "math.IT",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2023-03-13T16:02:18Z",
+    "updated_date": "2024-07-28T08:28:28Z",
+    "pdf_url": "https://arxiv.org/pdf/2303.07228v4",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2303.07228v4.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Heterotic Strings and Quantum Entanglement",
+    "authors": [
+      "Atish Dabholkar",
+      "Upamanyu Moitra"
+    ],
+    "abstract": "We construct $\\mathbb{Z}_N$ orbifolds of the ten-dimensional heterotic string theories appropriate for implementing the stringy replica method for the calculation of quantum entanglement entropy. A novel feature for the heterotic string is that the gauge symmetry must be broken by a Wilson line to ensure modular invariance. We completely classify the patterns of symmetry breaking. We show that the tachyonic contributions in all cases can be analytically continued, with a finite answer in the domain $0<N \\leq 1$, relevant for calculating entanglement entropy across the Rindler horizon. We discuss the physical implications of our results.",
+    "arxiv_id": "2407.17553v1",
+    "categories": [
+      "hep-th",
+      "gr-qc",
+      "math-ph",
+      "math.MP",
+      "quant-ph"
+    ],
+    "primary_category": "hep-th",
+    "published_date": "2024-07-24T18:00:01Z",
+    "updated_date": "2024-07-24T18:00:01Z",
+    "pdf_url": "https://arxiv.org/pdf/2407.17553v1",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2407.17553v1.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Random covariant quantum channels",
+    "authors": [
+      "Ion Nechita",
+      "Sang-Jun Park"
+    ],
+    "abstract": "The group symmetries inherent in quantum channels often make them tractable and applicable to various problems in quantum information theory. In this paper, we introduce natural probability distributions for covariant quantum channels. Specifically, this is achieved through the application of ``twirling operations'' on random quantum channels derived from the Stinespring representation that use Haar-distributed random isometries. We explore various types of group symmetries, including unitary and orthogonal covariance, hyperoctahedral covariance, diagonal orthogonal covariance (DOC), and analyze their properties related to quantum entanglement based on the model parameters. In particular, we discuss the threshold phenomenon for positive partial transpose and entanglement breaking properties, comparing thresholds among different classes of random covariant channels. Finally, we contribute to the PPT$^2$ conjecture by showing that the composition between two random DOC channels is generically entanglement breaking.",
+    "arxiv_id": "2403.03667v2",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.MP",
+      "math.PR"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2024-03-06T12:39:30Z",
+    "updated_date": "2024-07-18T19:33:05Z",
+    "pdf_url": "https://arxiv.org/pdf/2403.03667v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2403.03667v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Delayed Electron-Ion Entanglement Revealed with Zero Area Pulses",
+    "authors": [
+      "Axel Stenquist",
+      "Jan Marcus Dahlstr\u00f6m"
+    ],
+    "abstract": "The Grobe--Eberly doublet phenomenon occurs in photoelectron distributions when the remaining ion is dressed by a field. As was recently shown, the doublet can be interpreted as a signature of quantum entanglement between photoelectrons and strongly coupled ions. However, the dressed state nature of the ion prevents detection of the entanglement by straightforward coincidence detection. Here, we find that odd (zero-area) envelopes can substantially delay the generation of entanglement, but also modify the dynamics such that the doublet transforms into unique channel-resolved photoelectron distributions. Because these distributions can be used to correlate with the internal state of the ion, our proposed scheme opens up for detection of quantum entanglement, between photoelectrons and stongly-coupled ions, without a need for quantum phase measurements.",
+    "arxiv_id": "2405.03339v2",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.MP",
+      "physics.atom-ph",
+      "physics.comp-ph"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2024-05-06T10:39:25Z",
+    "updated_date": "2024-07-08T09:52:24Z",
+    "pdf_url": "https://arxiv.org/pdf/2405.03339v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2405.03339v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Exploring regular black holes within the framework of the TFD formalism",
+    "authors": [
+      "Jhonny A. A. Ruiz",
+      "A. F. Santos"
+    ],
+    "abstract": "In this paper, a massive scalar field non-minimally coupled with gravity is considered. Assuming a regular and spherically symmetric background, specifically a regular black hole solution, the energy-momentum tensor is calculated. Using the Thermo Field Dynamics (TFD) formalism and its topological structure, the corresponding Stefan-Boltzmann law and Casimir effect are investigated. The results for the regular black hole are compared with those obtained for the Schwarzschild black hole.",
+    "arxiv_id": "2407.00547v1",
+    "categories": [
+      "gr-qc",
+      "hep-th",
+      "math-ph",
+      "math.MP",
+      "quant-ph"
+    ],
+    "primary_category": "gr-qc",
+    "published_date": "2024-06-29T23:49:12Z",
+    "updated_date": "2024-06-29T23:49:12Z",
+    "pdf_url": "https://arxiv.org/pdf/2407.00547v1",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2407.00547v1.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Entanglement-invertible channels",
+    "authors": [
+      "Dominic Verdon"
+    ],
+    "abstract": "In a well-known result [Werner2001], Werner classified all tight quantum teleportation and dense coding schemes, showing that they correspond to unitary error bases. Here tightness is a certain dimensional restriction: the quantum system to be teleported and the entangled resource must be of dimension d, and the measurement must have d^2 outcomes.   In this work we generalise this classification so as to remove the dimensional restriction altogether, thereby resolving an open problem raised in that work. In fact, we classify not just teleportation and dense coding schemes, but entanglement-reversible channels. These are channels between finite-dimensional C*-algebras which are reversible with the aid of an entangled resource state, generalising ordinary reversibility of a channel.   In Werner's classification, a bijective correspondence between tight teleportation and dense coding schemes was shown: swapping Alice and Bob's operations turns a teleportation scheme into a dense coding scheme and vice versa. We observe that this property generalises ordinary invertibility of a channel; we call it entanglement-invertibility. We show that entanglement-invertible channels are precisely the quantum bijections previously studied in the setting of quantum combinatorics [Musto2018], which are classified in terms of the representation theory of the quantum permutation group.",
+    "arxiv_id": "2204.04493v4",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.MP",
+      "math.OA"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2022-04-09T15:19:43Z",
+    "updated_date": "2024-06-19T09:46:47Z",
+    "pdf_url": "https://arxiv.org/pdf/2204.04493v4",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2204.04493v4.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Topological Quantum Teleportation and Superdense Coding -- Without   Braiding",
+    "authors": [
+      "Sachin J. Valera"
+    ],
+    "abstract": "We present the teleportation and superdense coding protocols for a family of anyon theories coming from Tambara-Yamagami categories, of which the lowest rank theories describe Ising anyons. In contrast to the usual approach to anyonic computation, we relax the requirement that we should be able to braid anyons. This is motivated by the goal of designing basic protocols that require less control over quasiparticles, and which may therefore be amenable to realisation in near-term systems. Since these implementations are braid-free, they are also compatible with Majorana modes on a 1d quantum wire.",
+    "arxiv_id": "2303.17700v2",
+    "categories": [
+      "quant-ph",
+      "cond-mat.str-el",
+      "math-ph",
+      "math.MP",
+      "math.QA"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2023-03-30T20:46:29Z",
+    "updated_date": "2024-06-15T01:33:44Z",
+    "pdf_url": "https://arxiv.org/pdf/2303.17700v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2303.17700v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Multi-Unitary Complex Hadamard Matrices",
+    "authors": [
+      "Wojciech Bruzda",
+      "Grzegorz Rajchel-Mieldzio\u0107",
+      "Karol \u017byczkowski"
+    ],
+    "abstract": "We analyze the set of real and complex Hadamard matrices with additional symmetry constrains. In particular, we link the problem of existence of maximally entangled multipartite states of $2k$ subsystems with $d$ levels each to the set of complex Hadamard matrices of order $N=d^k$. To this end, we investigate possible subsets of such matrices which are, dual, strongly dual ($H=H^{\\rm R}$ or $H=H^{\\rm\\Gamma}$), two-unitary ($H^R$ and $H^{\\Gamma}$ are unitary), or $k$-unitary. Here $X^{\\rm R}$ denotes reshuffling of a matrix $X$ describing a bipartite system, and $X^{\\rm \\Gamma}$ its partial transpose. Such matrices find several applications in quantum many-body theory, tensor networks and classification of multipartite quantum entanglement and imply a broad class of analytically solvable quantum models in $1+1$ dimensions.",
+    "arxiv_id": "2306.00999v2",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.MP",
+      "05B20, 51F25, 46N50"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2023-05-30T20:11:18Z",
+    "updated_date": "2024-06-14T18:45:37Z",
+    "pdf_url": "https://arxiv.org/pdf/2306.00999v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2306.00999v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Efficient quantum circuits for port-based teleportation",
+    "authors": [
+      "Dmitry Grinko",
+      "Adam Burchardt",
+      "Maris Ozols"
+    ],
+    "abstract": "Port-based teleportation (PBT) is a variant of quantum teleportation that, unlike the canonical protocol by Bennett et al., does not require a correction operation on the teleported state. Since its introduction by Ishizaka and Hiroshima in 2008, no efficient implementation of PBT was known. We close this long-standing gap by building on our recent results on representations of partially transposed permutation matrix algebras and mixed quantum Schur transform. We construct efficient quantum algorithms for probabilistic and deterministic PBT protocols on $n$ ports of arbitrary local dimension, both for EPR and optimized resource states. We describe two constructions based on different encodings of the Gelfand-Tsetlin basis for $n$ qudits: a standard encoding that achieves $\\widetilde{O}(n)$ time and $O(n\\log(n))$ space complexity, and a Yamanouchi encoding that achieves $\\widetilde{O}(n^2)$ time and $O(\\log(n))$ space complexity, both for constant local dimension and target error. We also describe efficient circuits for preparing the optimal resource states.",
+    "arxiv_id": "2312.03188v2",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2023-12-05T23:39:04Z",
+    "updated_date": "2024-05-21T23:09:29Z",
+    "pdf_url": "https://arxiv.org/pdf/2312.03188v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2312.03188v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "A characterization of entangled two-qubit states via   partial-transpose-moments",
+    "authors": [
+      "Lin Zhang",
+      "Ming-Jing Zhao",
+      "Lin Chen",
+      "Hua Xiang",
+      "Yi Shen"
+    ],
+    "abstract": "Although quantum entanglement is an important resource, its characterization is quite challenging. The partial transposition is a common method to detect bipartite entanglement. In this paper, the authors study the partial-transpose(PT)-moments of two-qubit states,and completely describe the whole region, composed of the second and third PT-moments, for all two-qubit states. Furthermore, they determine the accurate region corresponding to all entangled two-qubit states. The states corresponding to those boundary points of the whole region, and to the border lines between separable and entangled states are analyzed. As an application, they characterize the entangled region of PT-moments for the two families of Werner states and Bell-diagonal states. The relations between entanglement and the pairs of PT-moments are revealed from these typical examples. They also numerically plot the whole region of possible PT-moments for all two-qubit X-states, and find that this region is almost the same as the whole region of PT-moments for all two-qubit states. Moreover, they extend their results to detect the entanglement of multiqubit states. By utilizing the PT-moment-based method to characterize the entanglement of the multiqubit states mixed by the GHZ and W states, they propose an operational way of verifying the genuine entanglement in such states.",
+    "arxiv_id": "2404.19308v1",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.MP",
+      "math.OC"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2024-04-30T07:28:09Z",
+    "updated_date": "2024-04-30T07:28:09Z",
+    "pdf_url": "https://arxiv.org/pdf/2404.19308v1",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2404.19308v1.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Critical Casimir effect in a disordered $O(2)$-symmetric model",
+    "authors": [
+      "G. O. Heymans",
+      "N. F. Svaiter",
+      "B. F. Svaiter",
+      "G. Krein"
+    ],
+    "abstract": "Critical Casimir effect appears when critical fluctuations of an order parameter interact with classical boundaries. We investigate this effect in the setting of a Landau-Ginzburg model with continuous symmetry in the presence of quenched disorder. The quenched free energy is written as an asymptotic series of moments of the models partition function. Our main result is that, in the presence of a strong disorder, Goldstone modes of the system contribute either with an attractive or with a repulsive force. This result was obtained using the distributional zeta-function method without relying on any particular ansatz in the functional space of the moments of the partition function.",
+    "arxiv_id": "2402.01588v2",
+    "categories": [
+      "cond-mat.soft",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "cond-mat.soft",
+    "published_date": "2024-02-02T17:28:46Z",
+    "updated_date": "2024-04-08T23:38:58Z",
+    "pdf_url": "https://arxiv.org/pdf/2402.01588v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2402.01588v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Qubits as Hypermatrices and Entanglement",
+    "authors": [
+      "Isaac Dobes",
+      "Naihuan Jing"
+    ],
+    "abstract": "In this paper, we represent $n$-qubits as hypermatrices and consider various applications to quantum entanglement. In particular, we use the higher-order singular value decomposition of hypermatrices to prove that the $\\pi$-transpose is an LU invariant. Additionally, through our construction we show that the matrix representation of the combinatorial hyperdeterminant of $2n$-qubits can be expressed as a product of the second Pauli matrix, allowing us to derive a formula for the combinatorial hyperdeterminant of $2n$-qubits in terms of the $n$-tangle.",
+    "arxiv_id": "2312.06944v3",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2023-12-12T02:47:27Z",
+    "updated_date": "2024-04-06T02:10:59Z",
+    "pdf_url": "https://arxiv.org/pdf/2312.06944v3",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2312.06944v3.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Thermal Area Law in Long-Range Interacting Systems",
+    "authors": [
+      "Donghoon Kim",
+      "Tomotaka Kuwahara",
+      "Keiji Saito"
+    ],
+    "abstract": "The area law of the bipartite information measure characterizes one of the most fundamental aspects of quantum many-body physics. In thermal equilibrium, the area law for the mutual information universally holds at arbitrary temperatures as long as the systems have short-range interactions. In systems with power-law decaying interactions, $r^{-\\alpha}$ ($r$: distance), conditions for the thermal area law are elusive. In this work, we aim to clarify the optimal condition $\\alpha> \\alpha_c$ such that the thermal area law universally holds. A standard approach to considering the conditions is to focus on the magnitude of the boundary interaction between two subsystems. However, we find here that the thermal area law is more robust than this conventional argument suggests. We show the optimal threshold for the thermal area law by $\\alpha_c= (D+1)/2$ ($D$: the spatial dimension of the lattice), assuming a power-law decay of the clustering for the bipartite correlations. Remarkably, this condition encompasses even the thermodynamically unstable regimes $\\alpha < D$. We verify this condition numerically, finding that it is qualitatively accurate for both integrable and non-integrable systems. Unconditional proof of the thermal area law is possible by developing the power-law clustering theorem for $\\alpha > D$ above a threshold temperature. Furthermore, the numerical calculation for the logarithmic negativity shows that the same criterion $\\alpha > (D+1)/2$ applies to the thermal area law for quantum entanglement.",
+    "arxiv_id": "2404.04172v1",
+    "categories": [
+      "quant-ph",
+      "cond-mat.stat-mech",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2024-04-05T15:32:14Z",
+    "updated_date": "2024-04-05T15:32:14Z",
+    "pdf_url": "https://arxiv.org/pdf/2404.04172v1",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2404.04172v1.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Building up quantum spacetimes with BCFT Legos",
+    "authors": [
+      "Ling-Yan Hung",
+      "Yikun Jiang"
+    ],
+    "abstract": "Is it possible to read off the quantum gravity dual of a CFT directly from its operator algebra? In this essay, we present a step-by-step recipe synthesizing results and techniques from conformal bootstrap, topological symmetries, tensor networks, a novel symmetry-preserving real-space renormalization algorithm devised originally in lattice models, and the asymptotics of quantum $6j$ symbols, thereby providing an answer in the affirmative. Quantum 2D Liouville theory serves as a simple and explicit example, illustrating how the quantum gravitational path integral can be built up from local pieces of BCFT correlation functions, which we call the ``BCFT Legos''. The constructive map between gravity and CFT naturally and explicitly bridges local geometrical data, algebraic structures, and quantum entanglement, as envisaged by the $\\it{It \\, from \\, Qubit}$ motto.",
+    "arxiv_id": "2404.00877v1",
+    "categories": [
+      "hep-th",
+      "cond-mat.str-el",
+      "gr-qc",
+      "math-ph",
+      "math.MP",
+      "quant-ph"
+    ],
+    "primary_category": "hep-th",
+    "published_date": "2024-04-01T03:14:36Z",
+    "updated_date": "2024-04-01T03:14:36Z",
+    "pdf_url": "https://arxiv.org/pdf/2404.00877v1",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2404.00877v1.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "2-Morita Equivalent Condensable Algebras in Topological Orders",
+    "authors": [
+      "Rongge Xu",
+      "Holiverse Yang"
+    ],
+    "abstract": "We classify $E_2$ condensable algebras in a modular tensor category $\\mathcal{C}$ up to 2-Morita equivalent. From physical perspective, it is equivalent to say we give the criterion when different $E_2$ condensable algebras result in a same condensed topological phase in a 2d anyon condensation process. By taking left and right centers of $E_1$ condensable algebras in $\\mathcal{C}$, we can exhaust all 2-Morita equivalent $E_2$ condensable algebras in $\\mathcal{C}$. This paper gives a complete interplay between $E_1$ condensable algebras in $\\mathcal{C}$, 2-Morita equivalent $E_2$ condensable algebras in $\\mathcal{C}$, and lagrangian algebras in $\\mathcal{C}\\boxtimes \\overline{\\mathcal{C}}$.   The relations between different condensable algebras can be translated to their module categories, which corresponds to the domain walls in topological orders. We introduce a two-step condensation process and study the fusion of domain walls. We also find an automorphism of an $E_2$ condensable algebra may lead to a non-trivial braided autoequivalence in the condensed phase. As concrete examples, we interpret the categories of quantum doubles of finite groups. We develop a lattice model depiction of $E_1$ condensable algebras, in which the role played by the left and right centers can be realized on a lattice model. Examples beyond group symmetries are also been discussed.   The classification of condensable algebras and domain walls motive us to introduce some promising concepts such as categorical quantum entanglement. Moreover, our results can be generalized to Witt equivalent modular tensor categories.",
+    "arxiv_id": "2403.19779v1",
+    "categories": [
+      "cond-mat.str-el",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "cond-mat.str-el",
+    "published_date": "2024-03-28T19:00:38Z",
+    "updated_date": "2024-03-28T19:00:38Z",
+    "pdf_url": "https://arxiv.org/pdf/2403.19779v1",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2403.19779v1.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Universal shot-noise limit for quantum metrology with local Hamiltonians",
+    "authors": [
+      "Hai-Long Shi",
+      "Xi-Wen Guan",
+      "Jing Yang"
+    ],
+    "abstract": "Quantum many-body interactions can induce quantum entanglement among particles, rendering them valuable resources for quantum-enhanced sensing. In this work, we derive a universal and fundamental bound for the growth of the quantum Fisher information. We apply our bound to the metrological protocol requiring only separable initial states, which can be readily prepared in experiments. By establishing a link between our bound and the Lieb-Robinson bound, which characterizes the operator growth in locally interacting quantum many-body systems, we prove that the precision cannot surpass the shot noise limit at all times in locally interacting quantum systems. This conclusion also holds for an initial state that is the non-degenerate ground state of a local and gapped Hamiltonian. These findings strongly hint that when one can only prepare separable initial states, nonlocal and long-range interactions are essential resources for surpassing the shot noise limit. This observation is confirmed through numerical analysis on the long-range Ising model. Our results bridge the field of many-body quantum sensing and operator growth in many-body quantum systems and open the possibility to investigate the interplay between quantum sensing and control, many-body physics and information scrambling",
+    "arxiv_id": "2308.03696v2",
+    "categories": [
+      "quant-ph",
+      "cond-mat.quant-gas",
+      "math-ph",
+      "math.MP",
+      "nlin.CD"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2023-08-07T16:13:01Z",
+    "updated_date": "2024-03-06T17:44:41Z",
+    "pdf_url": "https://arxiv.org/pdf/2308.03696v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2308.03696v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Holographic Limitations and Corrections to Quantum Information Protocols",
+    "authors": [
+      "Stefano Pirandola"
+    ],
+    "abstract": "We discuss the limitations imposed on entanglement distribution, quantum teleportation, and quantum communication by holographic bounds, such as the Bekenstein bound and Susskind's spherical entropy bound. For continuous-variable (CV) quantum information, we show how the naive application of holographic corrections disrupts well-established results. These corrections render perfect CV teleportation impossible, preclude uniform convergence in the teleportation simulation of lossy quantum channels, and impose a revised PLOB bound for quantum communication. While these mathematical corrections do not immediately impact practical quantum technologies, they are critical for a deeper theoretical understanding of quantum information theory.",
+    "arxiv_id": "2309.09939v4",
+    "categories": [
+      "quant-ph",
+      "hep-th",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2023-09-18T16:56:35Z",
+    "updated_date": "2024-02-14T10:47:08Z",
+    "pdf_url": "https://arxiv.org/pdf/2309.09939v4",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2309.09939v4.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Linearly coupled quantum harmonic oscillators and their quantum   entanglement",
+    "authors": [
+      "D. N. Makarov",
+      "K. A. Makarova"
+    ],
+    "abstract": "Quantum harmonic oscillators linearly coupled through coordinates and momenta, represented by the Hamiltonian $ {\\hat H}=\\sum^2_{i=1}\\left( \\frac{ {\\hat p}^{2}_i}{2 m_i } + \\frac{m_i \\omega^2_i}{2} x^2_i\\right) +{\\hat H}_{int} $, where the interaction of two oscillators ${\\hat H}_{int} = i k_1 x_1 { \\hat p }_2+ i k_2 x_2 {\\hat p}_1 + k_3 x_1 x_2-k_4 {\\hat p}_1 {\\hat p}_2$, found in many applications of quantum optics, nonlinear physics, molecular chemistry and biophysics. Despite this, there is currently no general solution to the Schr\\\"{o}dinger equation for such a system. This is especially relevant for quantum entanglement of such a system in quantum optics applications. Here this problem is solved and it is shown that quantum entanglement depends on only one coefficient $R \\in (0,1)$, which includes all the parameters of the system under consideration. It has been shown that quantum entanglement can be very large at certain values of this coefficient. The results obtained have a fairly simple analytical form, which facilitates analysis.",
+    "arxiv_id": "2402.00806v1",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2024-02-01T17:42:17Z",
+    "updated_date": "2024-02-01T17:42:17Z",
+    "pdf_url": "https://arxiv.org/pdf/2402.00806v1",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2402.00806v1.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Probing Quantum Entanglement from Quantum Correction to Newtonian   Potential Energy",
+    "authors": [
+      "A. Belhaj",
+      "S. E. Ennadifi",
+      "L. Jebli"
+    ],
+    "abstract": "Inspired by string theory ideas, we probe quantum entanglement from the gravitational potential energy. Concretely, we reconsider the study of quantum corrections to the Newtonian potential energy by treating a massive two-particle system $m_{1}$ and $m_{2}$ with size dimensions $r_{1}$ ad $% r_{2}$ where the two particles separated by a distance $d$ are under only their mutual classical gravitational interaction $V_{r}\\left( r_{1}\\text{, }% r_{2}\\right) $. Exploring such a size-dependent gravitational behavior and taking the limit $r_{1}$, $r_{2}\\ll d$, we investigate the associated quantum biparticle state and express its evolution after an interaction time $\\tau $. Among others, we show that the two masses cannot be separable due to the induced gravitational entanglement in terms of the accumulated quantum phase $\\delta \\phi =\\delta V_{g}\\tau /\\hbar $. By analogy with the classical gravity, we derive the expression of the resulting extremely weak entanglement force from the corresponding gravitational entanglement energy. Then, we provide certain entanglement diagnostics.",
+    "arxiv_id": "2401.14342v1",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2024-01-25T17:43:13Z",
+    "updated_date": "2024-01-25T17:43:13Z",
+    "pdf_url": "https://arxiv.org/pdf/2401.14342v1",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2401.14342v1.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Casimir effect of a rough membrane in 2+1 Horava-Lifshitz theory",
+    "authors": [
+      "Claudio B\u00f3rquez",
+      "Byron Droguett"
+    ],
+    "abstract": "We investigate the Casimir effect of a rough membrane within the framework of the Horava-Lifshitz theory in 2+1 dimensions. Quantum fluctuations are induced by an anisotropic scalar field subject to Dirichlet boundary conditions. We implement a coordinate transformation to render the membrane completely flat, treating the remaining terms associated with roughness as a potential. The spectrum is obtained through perturbation theory and regularized using the $\\zeta$--function method. We present an explicit example of a membrane with periodic border. Additionally, we consider the effect of temperature. Our findings reveal that the Casimir energy and force depend on roughness, the anisotropic scaling factor and temperature.",
+    "arxiv_id": "2312.01997v2",
+    "categories": [
+      "hep-th",
+      "gr-qc",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "hep-th",
+    "published_date": "2023-12-04T16:20:23Z",
+    "updated_date": "2024-01-25T15:02:18Z",
+    "pdf_url": "https://arxiv.org/pdf/2312.01997v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2312.01997v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "On the entanglement of co-ordinate and momentum degrees of freedom in   noncommutative space",
+    "authors": [
+      "Shilpa Nandi",
+      "Muklesur Rahaman",
+      "Pinaki Patra"
+    ],
+    "abstract": "In this paper, we investigate the quantum entanglement induced by phase-space noncommutativity. Both the position-position and momentum-momentum noncommutativity are incorporated to study the entanglement properties of coordinate and momentum degrees of freedom under the shade of oscillators in noncommutative space. Exact solutions for the systems are obtained after the model is re-expressed in terms of canonical variables, by performing a particular Bopp's shift to the noncommuting degrees of freedom. It is shown that the bipartite Gaussian state for an isotropic oscillator is always separable. To extend our study for the time-dependent system, we allow arbitrary time dependency on parameters. The time-dependent isotropic oscillator is solved with the Lewis-Riesenfeld invariant method. It turns out that even for arbitrary time-dependent scenarios, the separability property does not alter. We extend our study to the anisotropic oscillator, which provides an entangled state even for time-independent parameters. The Wigner quasi-probability distribution is constructed for a bipartite Gaussian state. The noise matrix (covariance matrix) is explicitly studied with the help of Wigner distribution. Simon's separability criterion (generalized Peres-Horodecki criterion) has been employed to find the unique function of the (mass and frequency) parameters, for which the bipartite states are separable. In particular, we show that the mere inclusion of non-commutativity of phase-space is not sufficient to generate the entanglement, rather anisotropy is important at the same footing.",
+    "arxiv_id": "2401.03014v1",
+    "categories": [
+      "quant-ph",
+      "hep-th",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2024-01-05T18:43:47Z",
+    "updated_date": "2024-01-05T18:43:47Z",
+    "pdf_url": "https://arxiv.org/pdf/2401.03014v1",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2401.03014v1.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Optimality of generalized Choi maps in $M_3$",
+    "authors": [
+      "Giovanni Scala",
+      "Anindita Bera",
+      "Gniewomir Sarbicki",
+      "Dariusz Chru\u015bci\u0144ski"
+    ],
+    "abstract": "A family of linear positive maps in the algebra of $3 \\times 3$ complex matrices proposed recently in Bera et al. arXiv:2212.03807 is further analyzed. It provides a generalization of a seminal Choi nondecomposable extremal map in $M_3$. We investigate when generalized Choi maps are optimal, i.e. cannot be represented as a sum of positive and completely positive maps. This property is weaker than extremality, however, it turns out that it plays a key role in detecting quantum entanglement.",
+    "arxiv_id": "2312.02814v1",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2023-12-05T14:57:11Z",
+    "updated_date": "2023-12-05T14:57:11Z",
+    "pdf_url": "https://arxiv.org/pdf/2312.02814v1",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2312.02814v1.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Entanglement of Sections: The pushout of entangled and parameterized   quantum information",
+    "authors": [
+      "Hisham Sati",
+      "Urs Schreiber"
+    ],
+    "abstract": "Recently Freedman & Hastings asked for a mathematical theory that would unify quantum entanglement/tensor-structure with parameterized/bundle-structure via their amalgamation (a hypothetical pushout) along bare quantum (information) theory. As a proposed answer to this question, we first make precise a form of the relevant pushout diagram in monoidal category theory. Then we prove that the pushout produces what is known as the *external* tensor product on vector bundles/K-classes, or rather on flat such bundles (flat K-theory), i.e., those equipped with monodromy encoding topological Berry phases. The bulk of our result is a further homotopy-theoretic enhancement of the situation to the \"derived category\" (infinity-category) of flat infinity-vector bundles (\"infinity-local systems\") equipped with the \"derived functor\" of the external tensor product. Concretely, we present an integral model category of simplicial functors into simplicial K-chain complexes which conveniently presents the infinity-category of parameterized HK-module spectra over varying base spaces and is equipped with homotopically well-behaved external tensor product structure. In concluding we indicate how this model category serves as categorical semantics for the linear-multiplicative fragment of Linear Homotopy Type Theory (LHoTT), which is thus exhibited as a universal quantum programming language. This is the context in which we recently showed that topological anyonic braid quantum gates are native objects in LHoTT.",
+    "arxiv_id": "2309.07245v2",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.AT",
+      "math.CT",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2023-09-13T18:28:43Z",
+    "updated_date": "2023-11-21T08:48:16Z",
+    "pdf_url": "https://arxiv.org/pdf/2309.07245v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2309.07245v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Quantum Wasserstein distance based on an optimization over separable   states",
+    "authors": [
+      "G\u00e9za T\u00f3th",
+      "J\u00f3zsef Pitrik"
+    ],
+    "abstract": "We define the quantum Wasserstein distance such that the optimization of the coupling is carried out over bipartite separable states rather than bipartite quantum states in general, and examine its properties. Surprisingly, we find that the self-distance is related to the quantum Fisher information. We present a transport map corresponding to an optimal bipartite separable state. We discuss how the quantum Wasserstein distance introduced is connected to criteria detecting quantum entanglement. We define variance-like quantities that can be obtained from the quantum Wasserstein distance by replacing the minimization over quantum states by a maximization. We extend our results to a family of generalized quantum Fisher information quantities.",
+    "arxiv_id": "2209.09925v3",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2022-09-20T18:01:33Z",
+    "updated_date": "2023-10-11T17:55:49Z",
+    "pdf_url": "https://arxiv.org/pdf/2209.09925v3",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2209.09925v3.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Fundamental limitations to key distillation from Gaussian states with   Gaussian operations",
+    "authors": [
+      "Ludovico Lami",
+      "Ladislav Mi\u0161ta, Jr.",
+      "Gerardo Adesso"
+    ],
+    "abstract": "We establish fundamental upper bounds on the amount of secret key that can be extracted from quantum Gaussian states by using only local Gaussian operations, local classical processing, and public communication. For one-way public communication, or when two-way public communication is allowed but Alice and Bob first perform destructive local Gaussian measurements, we prove that the key is bounded by the R\\'enyi-$2$ Gaussian entanglement of formation $E_{F,2}^{\\mathrm{\\scriptscriptstyle G}}$. Since the inequality is saturated for pure Gaussian states, this yields an operational interpretation of the R\\'enyi-$2$ entropy of entanglement as the secret key rate of pure Gaussian states that is accessible with Gaussian operations and one-way communication. In the general setting of two-way communication and arbitrary interactive protocols, we argue that $2 E_{F,2}^{\\mathrm{\\scriptscriptstyle G}}$ is still an upper bound on the extractable key. We conjecture that the factor of $2$ is spurious, which would imply that $E_{F,2}^{\\mathrm{\\scriptscriptstyle G}}$ coincides with the secret key rate of Gaussian states under Gaussian measurements and two-way public communication. We use these results to prove a gap between the secret key rates obtainable with arbitrary versus Gaussian operations. Such a gap is observed for states produced by sending one half of a two-mode squeezed vacuum through a pure loss channel, in the regime of sufficiently low squeezing or sufficiently high transmissivity. Finally, for a wide class of Gaussian states that includes all two-mode states, we prove a recently proposed conjecture on the equality between $E_{F,2}^{\\mathrm{\\scriptscriptstyle G}}$ and the Gaussian intrinsic entanglement. The unified entanglement quantifier emerging from such an equality is then endowed with a direct operational interpretation as the value of a quantum teleportation game.",
+    "arxiv_id": "2010.15729v2",
+    "categories": [
+      "quant-ph",
+      "cs.IT",
+      "math-ph",
+      "math.IT",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2020-10-29T16:26:46Z",
+    "updated_date": "2023-09-30T19:06:12Z",
+    "pdf_url": "https://arxiv.org/pdf/2010.15729v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2010.15729v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Simulating Entanglement beyond Quantum Steering",
+    "authors": [
+      "Yujie Zhang",
+      "Jiaxuan Zhang",
+      "Eric Chitambar"
+    ],
+    "abstract": "While quantum entanglement is a highly non-classical feature, certain entangled states cannot realize the nonlocal effect of quantum steering. In this work, we quantify the resource content of such states in terms of how much shared randomness is needed to simulate their dynamical behavior. We rigorously show that the shared randomness cost is unbounded even for some two-qubit unsteerable states. Moreover, the simulation cost for entangled states is always strictly greater than that of any separable state. Our work utilizes the equivalence between steering and measurement incompatibility, and it connects both to the zonotope approximation problem of Banach space theory.",
+    "arxiv_id": "2302.09060v2",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2023-02-17T18:52:33Z",
+    "updated_date": "2023-09-18T17:43:20Z",
+    "pdf_url": "https://arxiv.org/pdf/2302.09060v2",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2302.09060v2.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "Quantum teleportation and dynamics of quantum coherence and metrological   non-classical correlations for open two-qubit systems: A study of Markovian   and non-Markovian regimes",
+    "authors": [
+      "Yassine Dakir",
+      "Abdallah Slaoui",
+      "Abdel-Baset A. Mohamed",
+      "Rachid Ahl Laamara",
+      "Hichem Eleuch"
+    ],
+    "abstract": "We investigate the dynamics of non-classical correlations and quantum coherence in open quantum systems by employing metrics like local quantum Fisher information, local quantum uncertainty, and quantum Jensen-Shannon divergence. Our focus here is on a system of two qubits in two distinct physical situations: the first one when the two qubits are coupled to a single-mode cavity, while the second consists of two qubits immersed in dephasing reservoirs. Our study places significant emphasis on how the evolution of these quantum criterion is influenced by the initial state's purity (whether pure or mixed) and the nature of the environment (whether Markovian or non-Markovian). We observe that a decrease in the initial state's purity corresponds to a reduction in both quantum correlations and quantum coherence, whereas higher purity enhances these quantumness. Furthermore, we establish a quantum teleportation strategy based on the two different physical scenarios. In this approach, the resulting state of the two qubits functions as a quantum channel integrated into a quantum teleportation protocol. We also analyze how the purity of the initial state and the Markovian or non-Markovian regimes impact the quantum teleportation process.",
+    "arxiv_id": "2309.02149v1",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2023-09-05T11:41:04Z",
+    "updated_date": "2023-09-05T11:41:04Z",
+    "pdf_url": "https://arxiv.org/pdf/2309.02149v1",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2309.02149v1.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  },
+  {
+    "title": "On a gap in the proof of the generalised quantum Stein's lemma and its   consequences for the reversibility of quantum resources",
+    "authors": [
+      "Mario Berta",
+      "Fernando G. S. L. Brand\u00e3o",
+      "Gilad Gour",
+      "Ludovico Lami",
+      "Martin B. Plenio",
+      "Bartosz Regula",
+      "Marco Tomamichel"
+    ],
+    "abstract": "We show that the proof of the generalised quantum Stein's lemma [Brand\\~ao & Plenio, Commun. Math. Phys. 295, 791 (2010)] is not correct due to a gap in the argument leading to Lemma III.9. Hence, the main achievability result of Brand\\~ao & Plenio is not known to hold. This puts into question a number of established results in the literature, in particular the reversibility of quantum entanglement [Brand\\~ao & Plenio, Commun. Math. Phys. 295, 829 (2010); Nat. Phys. 4, 873 (2008)] and of general quantum resources [Brand\\~ao & Gour, Phys. Rev. Lett. 115, 070503 (2015)] under asymptotically resource non-generating operations. We discuss potential ways to recover variants of the newly unsettled results using other approaches.",
+    "arxiv_id": "2205.02813v4",
+    "categories": [
+      "quant-ph",
+      "math-ph",
+      "math.MP"
+    ],
+    "primary_category": "quant-ph",
+    "published_date": "2022-05-05T17:46:05Z",
+    "updated_date": "2023-08-25T11:04:32Z",
+    "pdf_url": "https://arxiv.org/pdf/2205.02813v4",
+    "local_pdf_path": "data\\arxiv\\pdfs\\mathematics\\2205.02813v4.pdf",
+    "comment": "",
+    "journal_ref": "",
+    "doi": ""
+  }
+]