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Using Grothendieck approach to the tensor product of locally convex spaces we review a characterization of positive maps as well as Belavkin-Ohya characterization of PPT states. Moreover, within this scheme, \textit{ a generalization of the idea of Choi matrices for genuine quantum systems will be presented}. |
A method for the determination of absolute quantum detection efficiency is suggested based on the measurement of photocount statistics of twin beams. The measured histograms of joint signal-idler photocount statistics allow to eliminate an additional noise superimposed on an ideal calibration field composed of only ph... |
Controllable multipartite entanglement is a crucial element in quantum information processing. Here we present a scheme that generates switchable bipartite and genuine tripartite entanglement between microwave and optical photons via an optoelectromechanical interface, where microwave and optical cavities are coupled ... |
The nonrelativistic Schroedinger equation for motion of a structureless particle in four-dimensional space-time entails a well-known expression for the conserved four-vector field of local probability density and current that are associated with a quantum state solution to the equation. Under the physical assumption t... |
We present an interaction scheme to control counter-rotating terms in the quantum Rabi model. We show that by applying a sequence of $\pi/2$ phase kicks to a two-level atom and a single mode quantized field, the natural dynamics of the Rabi model can be interrupted in a way that counter-rotating transitions can be sig... |
We consider the Wigner quasi-probability distribution function of a single mode of an electromagnetic or matter-wave field to address the question of whether a direct stochastic sampling and binning of the absolute square of the complex field amplitude can yield a distribution function $\tilde{P}_n$ that closely approx... |
A detailed derivation of the master equation of the cavity radiation of a coherently prepared $Y$-shaped four-level correlated emission laser is presented. The outline of the procedures that can be employed in analytically solving the stochastic differential equations and the rate equations of various correlations are... |
We propose a quantum representation of binary classification trees with binary features based on a probabilistic approach. By using the quantum computer as a processor for probability distributions, a probabilistic traversal of the decision tree can be realized via measurements of a quantum circuit. |
In this work, we construct the exact propagator for Dirac fermions in graphene-like systems immersed in external static magnetic fields with non-trivial spatial dependence. Such field profiles are generated within a first-order supersymmetric framework departing from much simpler (seed) magnetic field examples. |
Magic can be distributed non-locally in many-body entangled states, such as the low energy states of condensed matter systems. Using the Bravyi-Kitaev magic state distillation protocol, we find that non-local magic is distillable and can improve the distillation outcome. |
We analyze neutral atom Rydberg $C_Z$ gates based on adiabatic pulses applied symmetrically to both atoms. Analysis with smooth pulse shapes and Cs atom parameters predicts the gates can create Bell states with fidelity ${\mathcal F}>0.999$ using adiabatic rapid passage (ARP) pulses. |
Employing a recently proposed measure for quantum non-Markovianity, we carry out a systematic study of the size of memory effects in the spin-boson model for a large region of temperature and frequency cutoff parameters. The dynamics of the open system is described utilizing a second-order time-convolutionless master ... |
Relativistic fermionic field theories constitute the fundamental description of all observable matter. The simplest of the models provide a useful, classically verifiable benchmark for noisy intermediate scale quantum computers. |
The Talbot effect in quantum physics is known to produce intricate patterns in the probability distribution of a particle, known as "quantum carpets", corresponding to the revival and replication of the initial wave function. Recently, it was shown that one can encode a $D$-level qudit, in such a way that the ... |
Distributed quantum information processing is a promising platform for scaling up quantum information processing, where small- and intermediate-scale quantum devices are connected by a network of quantum channels for communicating quantum information, so as to cooperate in achieving larger-scale information processing.... |
Recent advances in quantum computing have brought us closer to realizing the potential of this transformative technology. While significant strides have been made in quantum error correction, many challenges persist, particularly in the realm of noise and scalability. |
Projective measurements of a single two-level quantum mechanical system (a qubit) evolving under a time-independent Hamiltonian produce a probability distribution that is periodic in the evolution time. The period of this distribution is an important parameter in the Hamiltonian. |
Knill demonstrated a fault-tolerant quantum computation scheme based on concatenated error-detecting codes and postselection with a simulated error threshold of 3% over the depolarizing channel. %We design a two-dimensional architecture for fault-tolerant quantum computation based on Knill's postselection scheme. |
A quantum computer based on an asymmetric coupled dot system has been proposed and shown to operate as the controlled-NOT-gate. The basic idea is (1) the electron is localized in one of the asymmetric coupled dots. |
Fidelity plays an important role in measuring distances between pairs of quantum states, of single as well as multiparty systems. Based on the concept of fidelity, we introduce a physical quantity, shared purity, for arbitrary pure or mixed quantum states of shared systems of an arbitrary number of parties in arbitrar... |
We report on an experimental observation of a two-photon ghost interference experiment. A distinguishing feature of our experiment is that the photons are generated via a non-degenerated spontaneous four-wave mixing process in a hot atomic ensemble; therefore the photon has narrow bandwidth. |
Exactly computing the full output distribution of linear optical circuits remains a challenge, as existing methods are either time-efficient but memory-intensive or memory-efficient but slow. Moreover, any realistic simulation must account for noise, and any viable quantum computing scheme based on linear optics requi... |
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number, even complete sets of such models. |
Towards realising larger scale quantum algorithms, the ability to prepare sizeable multi-qubit entangled states with full qubit control is used as a benchmark for quantum technologies. We investigate the extent to which entanglement is found within a prepared graph state on the 20-qubit superconducting quantum compute... |
Scrambling processes, which rapidly spread entanglement through many-body quantum systems, are difficult to investigate using standard techniques, but are relevant to quantum chaos and thermalization. In this Letter, we ask if quantum machine learning (QML) could be used to investigate such processes. |
Considering the intrinsic nonlinearity in a nanomechanical resonator coupled to a charge qubit, vacuum Rabi splitting effect is studied in a nanomechanical QED (qubit-resonator) system. A driven nonlinear Jaynes-Cummings model describes the dynamics of this qubit-resonator system. |
Secret sharing is a fundamental primitive in cryptography, and it can be achieved even with perfect security. However, the distribution of shares requires computational assumptions, which can compromise the overall security of the protocol. |
We present a protocol for measuring Bohmian - or the mathematically equivalent hydrodynamic - velocities based on an ensemble of two position measurements, defined from a Positive Operator Valued Measure, separated by a finite time interval. The protocol is very accurate and robust as long as the first measurement unc... |
A simple procedure to derive the transformation of a wavefunction under a change of reference frame is applied to some examples and its relation with the transformation of the Hamilton principal function is studied. |
We improve the test to show the impossibility of a quantum theory based on real numbers by a larger ratio of complex-to-real bound on a Bell-type parameter. In contrast to previous theoretical and experimental proposals the test requires three settings for the parties $A$ and $C$, but also six settings for the middle ... |
We introduce a set of Bell inequalities for a three-qubit system. Each inequality within this set is violated by all generalized GHZ states. |
We discuss the coherent splitting and recombining of a nanoparticle in a mesoscopic "closed-loop" Stern-Gerlach interferometer in which the observable is the spin of a single impurity embedded in the particle. This spin, when interacting with a pulsed magnetic gradient, generates the force on the particle. |
When a multi-qubit state evolves under local unitaries it may obtain a geometric phase, a feature dependent on the geometry of the state's projective Hilbert space. A correction term to this geometric phase in addition to the local subsystem phases may appear from correlations between the subsystems. |
A classical decision tree is completely based on splitting measures, which utilize the occurrence of random events in correspondence to its class labels in order to optimally segregate datasets. However, the splitting measures are based on greedy strategy, which leads to construction of an imbalanced tree and hence de... |
In his 1963 paper, Dirac [1] gave `A Remarkable Representation of the 3 + 2 de- Sitter Group'. We reproduce this representation using a generalised Jordan map which is motivated by the infinitesimal symplectic transformations related to the four dimensional symplectic group Sp(4). |
We have found that, in the intensity-dependent Jaynes-Cummings model, a field initially prepared in a statistical mixture of two coherent states, $|\alpha>$ and $|-\alpha>$, evolves toward a pure state. We have also shown that an even-coherent state turns periodically a into rotated odd-coherent state during the... |
We show the formation of Schrodinger cat-like states (SCLSs) during the spontaneous parametric down-conversion (SPDC) process when the pump mode is considered quantum and depleted. For the first time, we show the formation of SCLSs in the fundamental and second harmonic modes under non-dissipative and dissipative regi... |
Using the Green function approach to the problem of quantization of the phenomenological Maxwell theory, the propagation of quantized radiation through dispersive and absorptive multilayer dielectric plates is studied. Input--output relations are derived, with special emphasis on the determination of the quantum noise... |
We investigate the time-optimal control of the purification of a qubit interacting with a structured environment, consisting of a strongly coupled two-level defect in interaction with a thermal bath. On the basis of a geometric analysis, we show for weak and strong interaction strengths that the optimal control strate... |
We present the Random Permutation Sorting System (RPSS), a novel framework for true uniform randomness generation grounded in statistical quantum mechanics. RPSS is built on a pair of conjugate observables, the permutation count and the elapsed sorting time, whose heavy-tailed raw distributions synchronously converge ... |
Being a very promising technology, with impressive advances in the recent years, it is still unclear how quantum computing will scale to satisfy the requirements of its most powerful applications. Although continued progress in the fabrication and control of qubits is required, quantum computing scalability will depen... |
Spontaneous decay of an excited atom near a dispersing and absorbing microsphere of given complex permittivity that satisfies the Kramers-Kronig relations is studied, with special emphasis on a Drude-Lorentz permittivity. Both the whispering gallery field resonances below the band gap (for a dielectric sphere) and the... |
We study the entanglement effect of beam splitter on the temporally stable phase states. Specifically, we consider the eigenstates (phase states) of an unitary phase operator resulting from the polar decomposition of ladder operators of generalized Weyl--Heisenberg algebras possessing finite dimensional representation... |
The evolution of a quantum system towards thermal equilibrium is usually studied by approximate methods, which have their limits of validity and should be checked against analytically solvable models. In this paper, we propose an analytically solvable model to investigate the energy transfer between a bosonic bath and... |
Parameterized Quantum Circuits (PQCs) have been acknowledged as a leading strategy to utilize near-term quantum advantages in multiple problems, including machine learning and combinatorial optimization. When applied to specific tasks, the parameters in the quantum circuits are trained to minimize the target function.... |
The generalized amplitude damping channel (GADC) is one of the sources of noise in superconducting-circuit-based quantum computing. It can be viewed as the qubit analogue of the bosonic thermal channel, and it thus can be used to model lossy processes in the presence of background noise for low-temperature systems. |
The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilising the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and "po... |
We use quantum energy teleportation in the light-matter interaction as an operational means to create quantum field states that violate energy conditions and have negative local stress-energy densities. We show that the protocol is optimal in the sense that it scales in a way that saturates the quantum interest conjec... |
The scattering of electrons by an Aharonov--Bohm field is considered from the viewpoint of quantum-mechanical problem of constructing a self-adjoint Hamiltonian for the Pauli equation. The correct domain for the self-adjoint Hamiltonian, which takes into account explicitly the electron spin is found. |
We report an all-fiber-based experimental setup to generate a correlated photon-pair comb using Four Wave Mixing (FWM) in Highly Non-Linear Fiber (HNLF). Temporal correlations of the generated photons were confirmed through coincidence measurements. |
Bennett et al. proposed a family of protocols for entanglement distillation, namely, hashing, recurrence and breeding protocols. The last one is inferior to the hashing protocol in the asymptotic regime and has been investigated little. |
We construct, for any finite dimension $n$, a new hidden measurement model for quantum mechanics based on representing quantum transition probabilities by the volume of regions in projective Hilbert space. For $n=2$ our model is equivalent to the Aerts sphere model and serves as a generalization of it for dimensions $... |
Results of theoretical studies of the quantum unstable systems caused that there are rather widespread belief that a universal feature od the quantum decay process is the presence of three time regimes of the decay process: the early time (initial) leading to the Quantum Zeno (or Anti Zeno) Effects, "exponential... |
Non-Gaussian entangled states of light have been found to improve the success of quantum telepor- tation. Earlier works in the literature focussed mainly on two-mode non-Gaussian states generated by de-Gaussification of two-mode squeezed vacuum states. |
This work describes a series of experiments in IBM's 16-qubit Guadalupe quantum processor to find the ground state of various lattice systems implemented in the Qiskit library. We aim to design a Variational Quantum Eigensolver (QVE) resistant to noise and independent of the number of vertices in the lattice. |
The Ising chains in a transverse magnetic field of constant strength (h=1) and with the spin interaction value \lambda are considered. In the case of infinitely long chain, exact analytical expressions are found for the second central moment (dispersion) of the entropy operator S^\hat=-ln\rho with reduced density matr... |
Ray tracing algorithm is a category of rendering algorithms that calculate the color of pixels by simulating the physical movements of a huge amount of rays and calculating their energies, which can be implemented in parallel. Meanwhile, the superposition and entanglement property make quantum computing a natural fit ... |
The quantum phase transition of the Dicke-model has been observed recently in a system formed by motional excitations of a laser-driven Bose--Einstein condensate coupled to an optical cavity [1]. The cavity-based system is intrinsically open: photons can leak out of the cavity where they are detected. |
We propose a hybrid system with quantum mechanical three-body interactions between photons, phonons, and qubit excitations. These interactions take place in a circuit quantum electrodynamical architecture with a superconducting microwave resonator coupled to a transmon qubit whose shunt capacitance is free to mechanic... |
A second-order many-body perturbation correction to the relativistic Dirac-Hartree-Fock energy is evaluated stochastically by integrating 13-dimensional products of four-component spinors and Coulomb potentials. The integration in the real space of electron coordinates is carried out by the Monte Carlo (MC) method wit... |
Sampling unitary Fermionic Linear Optics (FLO), or matchgate circuits, has become a fundamental tool in quantum information. Such capability enables a large number of applications ranging from randomized benchmarking of continuous gate sets, to fermionic classical shadows. |
We establish and analyse the performance and resource requirements of an end-to-end fault-tolerant quantum algorithm for computing the absorption spectrum and population dynamics of photoexcited pyrazine. The quantum circuit construction consists of initial state preparation using uniformly controlled rotations, the t... |
The model of free charged Bosons in an external constant magnetic field inside a cylinder, one of the few locally gauge covariant systems amenable to analytic treatment, is rigorously investigated in the semiclassical approximation. The model was first studied by Schafroth and is suitable for the description of quasi-... |
We investigate the role of a time and spin-dependent phase shift on the evolution of one-dimensional discrete-time quantum walks. By employing Floquet engineering, a time and spin-dependent phase shift ($\phi$) is imprinted onto the walker's wave function while it shifts from one lattice site to another. |
Based on the interaction between different spatial modes, semiconductor Bragg-reflection waveguides provide a highly functional platform for non-linear optics. Therefore, the control and engineering of the properties of each spatial mode is essential. |
We study analytically the structure of an arbitrary order correlation function for a pair of Fock states and prove without any approximations that in a single measurement of particle positions interference effects must occur as experimentally observed with Bose-Einstein condensates. We also show that the noise level p... |
Geometric phases induced in quantum evolutions have built-in noise-resilient characters, and thus can find applications in many robust quantum manipulation tasks. Here, we propose a feasible and fast scheme for universal quantum computation on superconducting circuits with nonadiabatic non-Abelian geometric phases, us... |
As a genuine many-body entanglement, spin squeezing (SS) can be used to realize the highly precise measurement beyond the limit constrained by classical physics. Its generation has attracted much attention recently. |
A novel method for preparation of a single photon in temporally-delocalized entangled modes is proposed and analyzed. We show that two single-photon pulses propagating in a driven nonabsorbing medium with different group velocities are temporally split under parametric interaction into well-separated pulses. |
Quantum entanglement and quantum non-locality are known to exhibit monogamy, that is, they obey strong constraints on how they can be distributed among multipartite systems. Quantum correlations that comprise and go beyond entanglement are quantified by, e.g., quantum discord. |
Despite its putative robustness, the realization of and control over topological quantum matter is an ongoing grand challenge. Looking forward, robust characterization protocols are needed to first certify topological substrates before they are utilized in quantum algorithms. |
We study mechanical cooling in systems of coupled passive (lossy) and active (with gain) optical resonators. We find that for a driving laser which is red-detuned with respect to the cavity frequency, the supermode structure of the system is radically changed, featuring the emergence of genuine high-order exceptional ... |
We recently considered the task of summoning an unknown quantum state and proved necessary and sufficient conditions for Alice to be able to guarantee to complete the task when there may be several possible calls, of which she need only respond to one. We showed that these are strictly stronger conditions than those p... |
A PT-symmetric optically active medium that lases at the threshold gain also acts as a complete perfect absorber at the laser wavelength. This is because spectral singularities of PT-symmetric complex potentials are always accompanied by their time-reversal dual. |
We map a quantum Rabi ring, consisting of $N$ cavities arranged in a ring geometry, into an effective magnetic model containing the XY exchange and the Dzyaloshinskii Moriya (DM) interactions. The analogue of the latter is induced by an artificial magnetic field, which modulates photon hopping between nearest-neighbor... |
An automated and robust method for adiabatic population transfer and the preparation of an arbitrary quantum superposition state in atomic system using the oscillating dark states (ODS) is presented. Quantum state of a three-level $\Lambda$ configuration atomic system oscillates periodically between two ground levels,... |
We construct and analyze a family of low-density parity check (LDPC) quantum codes with a linear encoding rate, polynomial scaling distance and efficient decoding schemes. The code family is based on tessellations of closed, four-dimensional, hyperbolic manifolds, as first suggested by Guth and Lubotzky. |
Recent work by Renou et al. (2021) has led to some controversy concerning the question of whether quantum theory requires complex numbers for its formulation. We promote the view that the main result of that work is best understood not as a claim about the relative merits of different representations of quantum theory... |
We study the dynamics of the Gaudin magnet ("central-spin model") using machine-learning methods. This model is of practical importance, e.g., for studying non-Markovian decoherence dynamics of a central spin interacting with a large bath of environmental spins and for studies of nonequilibrium superconductivi... |
Large Language Models (LLMs) such as ChatGPT have transformed how we interact with and understand the capabilities of Artificial Intelligence (AI). However, the intersection of LLMs with the burgeoning field of Quantum Machine Learning (QML) is only in its nascent stages. |
A scheme for suppressing the correlated noise in signals transmitted over the bosonic Gaussian memory channels is proposed. This is a compromise solution rather than removing the noise completely. |
A. Peres constructed an example of particles entangled in the state of spin singlet. He claimed to have obtained the CHSH inequality and concluded that the violation of this inequality shows that in a measurement in which some variables are tested, other variables, not tested, have no defined value. |
We consider a class of large superposed states, obtained from dimer coverings on spin-1/2 isotropic lattices, whose potential usefulness ranges from organic molecules to quantum computation. We show that they are genuinely multiparty entangled, irrespective of the geometry and dimension of the isotropic lattice. |
Quantum error correction is important to quantum information processing, which allows us to reliably process information encoded in quantum error correction codes. Efficient quantum error correction benefits from the knowledge of error rates. |
We show that the time evolution of density operator of open qubit system can always be described in terms of the Kraus representation. A general scheme on how to construct the Kraus operators for an open qubit system is proposed, which can be generalized to open higher dimensional quantum systems. |
A method for constructing coherent states (CS) of finite-level systems with a given angular momentum is proposed. To this end we generalize the known spin equation (SE) to an infinite-dimensional Fock space. |
In this paper we theoretically investigate the magnomechanically induced transparency phenomenon and the slow/fast light effect in the situation where an atomic ensemble is placed inside the hybrid cavity of an opto-magnomechanical system. The system is driven by dual optical and phononic drives. |
Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models of relevance for the recent counterexamples to the minimum output entropy additi... |
We investigate the spontaneous emission from an inverted Y-type atomic system coupled by three coherent fields. We use the Schrödinger equation to calculate the probability amplitudes of the wave function of the system and derive an analytical expression of the spontaneous emission spectrum to trace the origin of the ... |
Finite-size error (FSE), the discrepancy between an observable in a finite system and in the thermodynamic limit, is ubiquitous in numerical simulations of quantum many body systems. Although a rough estimate of these errors can be obtained from a sequence of finite-size results, a strict, quantitative bound on the ma... |
We experimentally realize a high-intensity three-photon Greenberger-Horne-Zeilinger (GHZ) entanglement source directly following the proposal by Rarity and Tapster [J. G. Rarity and P. R. Tapster, Phys. Rev. A 59, R35 (1999)]. The threefold coincidence rate can be more than 200 Hz with a fidelity of 0.811, and the int... |
Expressions of several capacity regions in quantum information theory involve an optimization over auxiliary quantum registers. Evaluating such expressions requires bounds on the dimension of the Hilbert space of these auxiliary registers, for which no non-trivial technique is known; we lack a quantum analog of the Ca... |
Recent advances in the preparation, control and measurement of atomic gases have led to new insights into the quantum world and unprecedented metrological sensitivities, e.g. in measuring gravitational forces and magnetic fields. The full potential of applying such capabilities to areas as diverse as biomedical imagin... |
Zero knowledge plays a central role in cryptography and complexity. The seminal work of Ben-Or et al. (STOC 1988) shows that zero knowledge can be achieved unconditionally for any language in NEXP, as long as one is willing to make a suitable physical assumption: if the provers are spatially isolated, then they can be... |
A plane-wave approximation in particle physics implies that a width of a massive wave packet $\sigma_{\perp}$ is much larger than its Compton wavelength $\lambda_c = \hbar/mc$. For Gaussian beams or for packets with the non-singular phases (say, the Airy beams), corrections to this approximation are attenuated as $\la... |
Introduction (in German) to a novel approach to sector analysis in theories with long range forces which avoids notorious infrared problems; cf. <a href="https://arxiv.org/abs/1304.2794" data-arxiv-id="1304.2794" class="link-https">arXiv:1304.2794</a> |
Nonclassical states of light play a central role in many quantum information protocols. Their quantum features have been exploited to improve the readout of information from digital memories, modelled as arrays of microscopic beam splitters [S. Pirandola, Phys. Rev. Lett. 106, 090504 (2011)]. |
Solid-state quantum emitters, such as artificially engineered quantum dots or naturally occurring defects in solids, are being investigated for applications ranging from quantum information science and optoelectronics to biomedical imaging. Recently, these same systems have also been studied from the perspective of na... |
Control theory concerns with the question if and how it is possible to drive the behavior of a complex dynamical system. A system is said to be controllable if we can drive it from any initial state to any desired final state in finite time. |
Representation of the quantum measurement with the help of non-orthogonal decomposition of unit is presented in the paper for the first time. Methods for solution of the quantum detection and measurement problems based on the suggested representation are proposed, as well. |
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