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Starting with the valence bond solid (VBS) ground state of the 1D AKLT Hamiltonian, we make a partition of the system in 2 subsystems $A$ and $B$, where $A$ is a block of $L$ consecutive spins and $B$ is it's complement. In that setting we compute the partial transpose density matrix with respect to $A$, $\rho^{T_...
In this paper, we report findings of non-stationary behavior observed in a fully connected qubit network, utilizing a random unitary evolution model in open quantum system theory. The environmental effect is reflected in the partial swap (PSW) interaction between pairs of qubits with a certain probability.
By exploiting the hyperentanglement, we propose a new concrete scheme to realize weak value amplification, which can be implemented by N hyperentangled photons along with coincidence detection. Our scheme can optimally increase the amplification factor by a factor of N compared to the usage of N uncorrelated photons, ...
In this thesis we will work under the premises of the Cellular Automata Interpretation of QM, by Gerard 't Hooft, according to whom particles evolve following the rules of Cellular Automata (CA), a mathematical model consisting of discrete units that evolve following deterministic laws in discrete space and time. ...
We report on the realization of an all-optical transistor by mapping gate and source photons into strongly interacting Rydberg excitations with different principal quantum numbers in an ultracold atomic ensemble. We obtain a record switch contrast of 40 % for a coherent gate input with mean photon number one and demon...
Accurate assessment and management of errors is indispensable for extracting useful results from noisy intermediate-scale quantum (NISQ) devices. In this work, we propose the qubit error probability (QEP), a device specific metric that combines relaxation, dephasing, gate, and measurement contributions into a single p...
Bayesian learning is ubiquitous for implementing classification and regression tasks, however, it is accompanied by computationally intractable limitations when the feature spaces become extremely large. Aiming to solve this problem, we develop a quantum bayesian learning framework of the restricted Boltzmann machine ...
Quantum interfaces (QIs) that generate entanglement between a multimode atomic memory and a photon forms a multiplexed repeater node and hold promise to greatly improve quantum repeater rates. Recently, the temporal multimode spin-wave memory that is entangled with a photon has been demonstrated with cold atoms.
The integrated information theory is thought to be a key clue towards the theoretical understanding of consciousness. In this study, we propose a simple numerical model comprising a set of coupled double quantum dots, where the disconnection of the elements is represented by the removal of Coulomb interaction between ...
We demonstrate nonlocal modulation of entangled photons with truly distributed RF clocks. Leveraging a custom radio-over-fiber (RFoF) system characterized via classical spectral interference, we validate its effectiveness for quantum networking by multiplexing the RFoF clock with one photon from a frequency-bin-entang...
High harmonic generation is a resource of extremely broad frequency combs of ultrashort light pulses. The non-classical nature of this new quantum source has been recently evidenced in semiconductors by showing that high harmonic generation generates multimode squeezed states of light.
The subject of controlling quantum systems is not new, but concepts that have been introduced in the last decade and a half, especially that of coherent feedback, suggest new questions that broaden and deepen the field. Here we provide a concise overview and definition of quantum feedback control, both coherent and me...
Recently a method for adiabatic quantum computation has been proposed and there has been considerable speculation about its efficiency for NP-complete problems. Heuristic arguments in its favor are based on the unproven assumption of an eigenvalue gap.
Quantum key-distribution protocols allow two honest distant parties to establish a common truly random secret key in the presence of powerful adversaries, provided that the two users share beforehand a short secret key. This pre-shared secret key is used mainly for authentication purposes in the post-processing of cla...
The Klein paradox is reassessed by considering the properties of a finite square well or barrier in the Dirac equation. It is shown that spontaneous positron emission occurs for a well if the potential is strong enough.
Quantum computing, along with quantum metrology and quantum communication, are disruptive technologies that promise, in the near future, to impact different sectors of academic research and industry. Among the computational challenges with great interest in science and industry are the inversion problems.
Some critical open problems of epistemic logics can be investigated in the framework of a quantum computational approach. The basic idea is to interpret sentences - like Alice knows that Bob does not understand that Pi is irrational - as pieces of quantum information (generally represented by density operators of conv...
Cavity electro-(opto-)mechanics allows us to access not only single isolated but also multiple mechanical modes in a massive object. Here we develop a multi-mode electromechanical system in which a several membrane vibrational modes are coupled to a three-dimensional loop-gap superconducting microwave cavity.
We study a quantum computing system using microwave photons in transmission line resonators on a superconducting chip as qubits. We show that all control necessary for quantum computing can be implemented by coupling to Josephson devices on the same chip, and take advantage of their strong inherent nonlinearities to r...
We suggest generalized robustness for quantifying nonlocality and derive its equivalence to the maximum violation ratio of Bell inequalities defined as vectors with non-negative elements. We investigate its properties by comparing it with white-noise and standard robustness measures.
Stabilizer Entropy (SE) quantifies the spread of a state in the basis of Pauli operators. It is a computationally tractable measure of non-stabilizerness and thus a useful resource for quantum computation.
Heat and pressure are ultimately transmitted via quantized degrees of freedom, like gas particles and phonons. While a continuous Brownian description of these noise sources is adequate to model measurements with relatively long integration times, sufficiently precise measurements can resolve the detailed time depende...
In this paper, we analyze the potential for new types of searches using the formalism of scattering random walks on Quantum Computers. Given a particular type of graph consisting of nodes and connections, a "Tree Maze", we would like to find a selected final node as quickly as possible, faster than any classic...
Solving linear and nonlinear differential equations with large degrees of freedom is an important task for scientific and industrial applications. In order to solve such differential equations on a quantum computer, it is necessary to embed classical variables into a quantum state.
Scalable quantum networks rely on optical connections between long-lived qubits to distribute entanglement. Tin vacancies in diamond have emerged as promising long-lived qubits, offering extended spin coherence times at liquid helium temperatures and spin-dependent, highly coherent optical transitions for effective ph...
We investigate the problem of the existence of a density matrix rho on the product of three Hilbert spaces with given marginals on the pair (1,2) and the pair (2,3). While we do not solve this problem completely we offer partial results in the form of some necessary and some sufficient conditions on the two marginals....
Preparing the ground state of a system is an important task in physics. We propose a quantum algorithm for preparing the ground state of a physical system that can be simulated on a quantum computer.
Superconducting quantum devices are a leading technology for quantum computation, but they suffer from several challenges. Gate errors, coherence errors and a lack of connectivity all contribute to low fidelity results.
Quantum walks contribute significantly to developing quantum algorithms and quantum simulations. Here, we introduce a first of its kind one-dimensional quantum walk in the $d$-dimensional quantum domain, where $d>2$, and show its equivalence for circuit realization in an arbitrary finite-dimensional quantum logic f...
Noise in quantum hardware remains the biggest roadblock for the implementation of quantum computers. To fight the noise in the practical application of near-term quantum computers, instead of relying on quantum error correction which requires large qubit overhead, we turn to quantum error mitigation, in which we make ...
We extend the tools of quantum resource theories to scenarios in which multiple quantities (or resources) are present, and their interplay governs the evolution of physical systems. We derive conditions for the interconversion of these resources, which generalise the first law of thermodynamics.
Algorithmic discrepancy theory seeks efficient algorithms to find those two-colorings of a set that minimize a given measure of coloring imbalance in the set, its {\it discrepancy}. The {\it Euclidean discrepancy} problem and the problem of balancing covariates in randomized trials have efficient randomized algorithms...
The magnetic Otto thermal machine based on a two-spin-1/2 XYZ working fluid in the presence of an inhomogeneous magnetic field and antisymmetric Dzyaloshinsky--Moriya (DM) and symmetric Kaplan--Shekhtman--Entin-Wohlman--Aharony (KSEA) interactions is considered. Its possible modes of operation are found and classified...
Given $n$ linearly independent pure states and their prior probabilities, we study the problem of optimum unambiguous discrimination of these states. We derive the properties of the optimum solution and the equations that must be satisfied by the optimum measurement strategy which achieves the maximum average success ...
Fabrication processes involving anhydrous hydrofluoric vapor etching are developed to create high-$Q$ aluminum superconducting microwave resonators on free-standing silicon membranes formed from a silicon-on-insulator wafer. Using this fabrication process, a high-impedance $8.9$GHz coil resonator is coupled capacitive...
We investigate the teleportation of a quantum state using a three-particle entangled W state. We compare and contrast our results with those in Ref.
In quantum computing architectures, one important factor is the trade-off between the need to couple qubits to each other and to an external drive and the need to isolate them well enough in order to protect the information for an extended period of time. In the case of superconducting circuits, one approach is to uti...
The central physical concepts and mathematical techniques used in the theory of open quantum systems are reviewed. Particular emphasis is laid on the interrelations of apparently different approaches.
Exploiting quantum effects of mechanical motion, such as backaction evading measurements or squeezing, requires preparation of the oscillator in a high-purity state. The largest state purities in optomechanics to date have relied on cryogenic cooling, combined with coupling to electromagnetic resonators driven with a ...
The Trotter-Suzuki decomposition is a promising avenue for digital quantum simulation (DQS), approximating continuous-time dynamics by discrete Trotter steps of duration $\tau$. Recent work suggested that DQS is typically characterized by a sharp Trotter transition: when $\tau$ is increased beyond a threshold value, a...
We report on the realization of Bose-Einstein condensation of metastable helium-4. After exciting helium to its metastable state in a novel pulse-tube cryostat source, the atomic beam is collimated and slowed.
We calculate the correlation functions of strings of spin operators for integrable quantum circuits exactly. These observables can be used for calibration of quantum simulation platforms.
In 1981, Takeuti introduced quantum set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed linear subspaces of a Hilbert space in a manner analogous to Boolean-valued models of set theory, and showed that appropriate counterparts of the axioms of Zermelo-Fraenkel se...
Single-photon detectors are ``blind" after the detection of a photon, and thereafter display a characteristic recovery in efficiency, during which the number of undetected photons depends on the statistics of the incident light. We show how the efficiency-recovery, photon statistics and intensity have an interdepe...
In one dimension one can dissect a scattering potential $ v(x) $ into pieces $ v_i(x) $ and use the notion of the transfer matrix to determine the scattering content of $ v(x) $ from that of $ v_i(x) $. This observation has numerous practical applications in different areas of physics.
We develop a general theory describing the thermodynamical behavior of open quantum systems coupled to thermal baths beyond perturbation theory. Our approach is based on the exact time-local quantum master equation for the reduced open system states, and on a principle of minimal dissipation.
Understanding quantum noise is an essential step towards building practical quantum information processing systems. Pauli noise is a useful model that has been widely applied in quantum benchmarking, error mitigation, and error correction.
Bohmian mechanics provides an explanation of quantum phenomena in terms of point particles guided by wave functions. This review focuses on the formalism of non-relativistic Bohmian mechanics, rather than its interpretation.
Operations performing on quantum batteries are extended to scenarios where we no longer force the existence of definite causal order of occurrence between distinct processes. In contrast to standard theories, the so called indefinite causal order is found to have the capability of accomplishing tasks that are not poss...
We numerically study the one-dimensional long-range Transverse Field Ising Model (TFIM) in the antiferromagnetic (AFM) regime at zero temperature using Generalized Hartree-Fock (GHF) theory. The spin-spin interaction extends to all spins in the lattice and decays as $1/r^\alpha$, where $r$ denotes the distance between...
So far, superconducting quantum computers have certain constraints on qubit connectivity, such as nearest-neighbor couplings. To overcome this limitation, we propose a scalable architecture to simultaneously connect several pairs of distant qubits via a dispersively coupled quantum bus.
Quantum Optimal Control (QOC) enables the realization of accurate operations, such as quantum gates, and support the development of quantum technologies. To date, many QOC frameworks have been developed but those remain only naturally suited to optimize a single targeted operation at a time.
Single-photon sources are necessary components for many prospective quantum technologies. One candidate for a single-photon source is spontaneous parametric down conversion combined with a heralding photon detection.
Gleason-type theorems for quantum theory allow one to recover the quantum state space by assuming that (i) states consistently assign probabilities to measurement outcomes and that
An alternative kind of deleting/erasing operation is introduced which differs from the commonly used {\it controlled-not} (C-not) conditional logical operation $-$to flip to a standard, `zero' value the (classical or quantum) state of the last copy in a chain, in a deletion process. It is completely reversible, in...
We report the first demonstration of quantum interference in multimode interference (MMI) devices and a new complete characterization technique that can be applied to any photonic device that removes the need for phase stable measurements. MMI devices provide a compact and robust realization of NxM optical circuits, w...
We provide a generalization of the idea of unitary designs to cover finite averaging over much more general operations on quantum states. Namely, we construct finite averaging sets for averaging quantum states over arbitrary reductive Lie groups, on condition that the averaging is performed uniformly over the compact ...
In this paper we formulate limit Zeno dynamics of general open systems as the adiabatic elimination of fast components. We are able to exploit previous work on adiabatic elimination of quantum stochastic models to give explicitly the conditions under which open Zeno dynamics will exist.
We present a stack model for breaking down the complexity of entanglement-based quantum networks. More specifically, we focus on the structures and architectures of quantum networks and not on concrete physical implementations of network elements.
We report the suitability of an Einstein-Podolsky-Rosen (EPR) entanglement source for gaussian continuous-variable quantum key distribution at 1550 nm. Our source is based on a single continuous-wave squeezed vacuum mode combined with a vacuum mode at a balanced beam splitter.
Quantum technologies based on the particle nature of a photon has been progressed over the last several decades, where the fundamental quantum feature of entanglement has been tested by Hong-Ou-Mandel (HOM) type anticorrelation as well as Bell-type nonlocal correlation. Mutually exclusive quantum natures of the wave-p...
We propose a polarization to orbital angular momentum teleportation scheme using entangled photon pairs generated by spontaneous parametric down conversion. By making a joint detection of the polarization and angular momentum parity of a single photon, we are able to detect all the Bell-states and perform, in principl...
Measurement incompatibility describes two or more quantum measurements whose expected joint outcome on a given system cannot be defined. This purely non-classical phenomenon provides a necessary ingredient in many quantum information tasks such violating a Bell Inequality or nonlocally steering part of an entangled st...
We study non-Markovian effects present in a driven qubit coupled to a finite environment using a recently proposed model developed in the context of calorimetric measurements of open quantum systems. To quantify the degree of non-Markovianity we use the Breuer-Laine-Piilo (BLP) measure [Breuer \textit{et al.
This thesis is devoted to studying two tasks: refrigeration and the creation of correlations. In the refrigeration part, two different paradigms of cooling, namely coherent and incoherent, are defined.
Adaptive variational algorithms suffer from prohibitively high measurement costs during the generator selection step, since energy gradients must be estimated for a large operator pool. This scaling bottleneck limits their applicability to larger molecular systems on near-term quantum devices.
Entropic dynamics of a multiqubit cavity quantum electrodynamics system is simulated and various aspects of entropy are explored. In the modified version of the Tavis-Cummings-Hubbard model, atoms are held in optical cavities through optical tweezers and can jump between different cavities through the tunneling effect...
We analyzed the efficiency of coherent population trapping (CPT) in a superposition of the ground states of three-level atoms under the influence of the decoherence process induced by a broadband thermal field. We showed that in a single atom there is no perfect CPT when the atomic transitions are affected by the ther...
Trace decreasing dynamical maps are as physical as trace preserving ones; however, they are much less studied. Here we overview how the quantum Sinkhorn theorem can be successfully applied to find a two-qubit entangled state which has the strongest robustness against local noises and losses of quantum information carr...
Spin defects in silicon carbide (SiC) have attracted increasing interest due to their excellent optical and spin properties, which are useful in quantum information processing. In this paper, we systematically investigate the temperature dependence of the spin properties of divacancy defects in implanted 4\emph{H}-SiC...
We have studied a relativistic electron in the presence of a uniform magnetic field and scalar potential in the cosmic string spacetime. The exact solutions of the Dirac equation with a Coulomb-like scalar potential and linear vector potential through the gravitational fields are found using SU(1,1) Lie algebras.
We investigate the relation between the scaling of block entropies and the efficient simulability by Matrix Product States (MPS), and clarify the connection both for von Neumann and Renyi entropies (see Table I). Most notably, even states obeying a strict area law for the von Neumann entropy are not necessarily approx...
Error filtration is a method for encoding the quantum state of a single particle into a higher dimensional Hilbert space in such a way that it becomes less sensitive to phase noise. We experimentally demonstrate this method by distributing a secret key over an optical fiber whose noise level otherwise precludes secure...
A time-dependent finite-state Markov chain that uses doubly stochastic transition matrices, is considered. Entropic quantities that describe the randomness of the probability vectors, and also the randomness of the discrete paths, are studied.
We consider measurements, described by a positive-operator-valued measure (POVM), whose outcome probabilities determine an arbitrary pure state of a D-dimensional quantum system. We call such a measurement a pure-state informationally complete (PSI-complete) POVM.
Flat-band systems provide an ideal platform for exploring exotic quantum phenomena, where the strongly suppressed kinetic energy in these flat energy bands suggests the potential for exotic phases driven by geometric structure, disorder, and interactions. While intriguing phenomena and physical mechanisms have been un...
How the thermodynamic entropy $S_{TD}$ is related to the Boltzmann entropy $S_{B}$ has been one of the central issues since the beginning of statistical mechanics. Today, it is believed that the thermodynamic entropy $S_{TD}$ is equal to a function $\tilde{S}_{B}$ that is defined by regularizing the Boltzman entropy i...
We propose a quantum measurement that probabilistically projects a pair of qudits of dimension $d$ onto a Bell state in a two-qubit subspace. It can be performed using linear-optical circuits with the success probabilities of $1-d^{-1}$ without ancilla photons and $1-d^{-(k+1)}$ with $2(2^{k}-1)$ ancilla photons.
We present an efficient quantum algorithm for the exact evaluation of either the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function Z for a family of graphs related to irreducible cyclic codes. This problem is related to the evaluation of the Jones and Tutte polynomials.
As the minituarization of electronic devices, which are sensitive to temperature, grows apace, sensing of temperature with ever smaller probes is more important than ever. Genuinely quantum mechanical schemes of thermometry are thus expected to be crucial to future technological progress.
An explicit Lagrangian description is given for the Heisenberg equation on the algebra of operators of a quantum system, and for the Landau-von Neumann equation on the manifold of quantum states which are isospectral with respect to a fixed reference quantum state.
Wave-particle duality as one of the expression of Bohr complementarity is a significant concept in the field of quantum mechanics. Quantitative analysis of wave-particle duality aims to establish a complementary relation between the particle and wave properties.
The novel concept of quantum logical entropy is presented and analyzed. We prove several basic properties of this entropy with regard to density matrices.
Quantum feedback is a technique for measuring a qubit and applying appropriate feedback depending on the measurement results. Here, we propose a new on-chip quantum feedback method where the measurement-result information is not taken from the chip to the outside of a dilution refrigerator.
We present a generic model of coupling quantum optical and solid state qubits, and the corresponding transfer protocols. The example discussed is a trapped ion coupled to a charge qubit (e.g. Cooper pair box).
The advent of structured, high-dimensional entangled states brings new possibilities for quantum imaging, information processing and quantum key distribution. We experimentally generate and characterize a spatially entangled state stored in a quantum memory system, using entropic EPR-steering inequality, yielding genu...
The gravitationally induced entanglement is a type of quantum entanglement that can be generated between two mesoscopic particles using their Newtonian gravitational interaction. It has attracted a great deal of attention as a new platform for studying quantum aspects of gravity.
In the spirit of device-independent cryptography, we present a two-party quantum authorization primitive with non-locality as its fueling resource. Therein, users are attributed authorization levels granting them access to a private database accordingly.
This is a slightly extended version of a review of Adam Becker's book What is Real? The Unfinished Quest for the Meaning of Quantum Physics, to appear in American Journal of Physics.
Quantum decoherence due to imperfect manipulation of quantum devices is a key issue in the noisy intermediate-scale quantum (NISQ) era. Standard analyses in quantum information and quantum computation use error rates to parameterize quantum noise channels.
The quantum repeater protocol is a promising approach to implement long-distance quantum communication and large-scale quantum networks. A key idea of the quantum repeater protocol is to use long-lived quantum memories to achieve efficient entanglement connection between different repeater segments with a polynomial s...
We introduce a quantum channel to model the dissipative dynamics resulting from the coupling between spin and motional degrees of freedom in chains of neutral atoms with Rydberg interactions. The quantum channel acts on the reduced spin state obtained under the frozen gas approximation, modulating its elements with ti...
Continuous variable quantum key distribution (CV-QKD) is a promising emerging technology for the distribution of secure keys for symmetric encryption. It can be readily implemented using commercial off-the-shelf optical telecommunications components.
Efficient methods for the representation and simulation of quantum states and quantum operations are crucial for the optimization of quantum circuits. Decision diagrams (DDs), a well-studied data structure originally used to represent Boolean functions, have proven capable of capturing relevant aspects of quantum syst...
We study the quantum thermodynamics of a coherent macroscopic electromagnetic field (laser) coupled to a two-level system (qubit) near resonance, from weak to strong driving regimes. This combined system is, in turn, weakly coupled to a thermal radiation field, and can be described by an autonomous quantum master equa...
The connection between spin and symmetry was established by Wigner in his 1939 paper on the Poincaré group. For a massive particle at rest, the little group is O(3) from which the concept of spin emerges.
Exploitation of time-frequency properties of SPDC photon pairs has recently found application in many endeavors. Complete characterization and control over the states in this degree of freedom is of paramount importance for the development of optical quantum technologies.
The Nikiforov-Uvarov method is a simple, yet elegant and powerful method for solving second-order differential equations of generalized hypergeometric type. In the past, it has been used to solve many problems in quantum mechanics and elsewhere.
We study the performance of distance-three surface code layouts under realistic multi-parameter noise models. We first calculate their thresholds under depolarizing noise.
The geometric phases of a two-level atom interacting with non-Markovian environments are calculated and the non-Markovian effects on the geometric phases are discussed in this paper. Three kinds of methods that describe the non-Markovian process, projection superoperator technique, memory kernel master equation and po...

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