Degree Of Quantum Entanglement Research Articles

Quantum correlations and entanglement in coupled optomechanical resonators with photon hopping via Gaussian interferometric power analysis

Quantum correlations that surpass entanglement are of great importance in the realms of quantum information processing and quantum computation. Essentially, for quantum systems prepared in pure states, it is difficult to differentiate between quantum entanglement and quantum correlation. Nonetheless, this indistinguishability is no longer holds for mixed states. To contribute to a better understanding of this differentiation, we have explored a simple model for both generating and measuring these quantum correlations. Our study concerns two macroscopic mechanical resonators placed in separate Fabry–Pérot cavities, coupled through the photon hopping process. this system offers a comprehensively way to investigate and quantify quantum correlations beyond entanglement between these mechanical modes. The key ingredient in analyzing quantum correlation in this system is the global covariance matrix. It forms the basis for computing two essential metrics: the logarithmic negativity ( ENm ) and the Gaussian interferometric power ( PGm ). These metrics provide the tools to measure the degree of quantum entanglement and quantum correlations, respectively. Our study reveals that the Gaussian interferometric power ( PGm ) proves to be a more suitable metric for characterizing quantum correlations among the mechanical modes in an optomechanical quantum system, particularly in scenarios featuring resilient photon hopping.

Square Root Statistics of Density Matrices and Their Applications.

To estimate the degree of quantum entanglement of random pure states, it is crucial to understand the statistical behavior of entanglement indicators such as the von Neumann entropy, quantum purity, and entanglement capacity. These entanglement metrics are functions of the spectrum of density matrices, and their statistical behavior over different generic state ensembles have been intensively studied in the literature. As an alternative metric, in this work, we study the sum of the square root spectrum of density matrices, which is relevant to negativity and fidelity in quantum information processing. In particular, we derive the finite-size mean and variance formulas of the sum of the square root spectrum over the Bures-Hall ensemble, extending known results obtained recently over the Hilbert-Schmidt ensemble.

The dynamics of a quantum Cournot duopoly with asymmetric information and heterogeneous players

In this paper, the dynamics of a quantum Cournot duopoly with asymmetric information and heterogeneous players in discrete time is established by combining the quantum games and chaotic dynamics theory. Theoretical results on the local stability of the quantum Bayes-Nash equilibria are obtained by analysis. In addition, the nonlinear dynamical behaviors are discussed by numerical simulations. The simulation results indicate that increasing the degree of quantum entanglement can delay the occurrence of bifurcation, in the case of a high possibility of low cost. And a larger quantum entanglement delays the chaos at the same quantum strategy adjustment speed. The market failure caused by high costs can be regulated by appropriately adjusting the degree of quantum entanglement.

Chaotic dynamics of a quantum Cournot duopoly game with heterogeneous expectations

On the basis of the bounded rationality and adaptive expectations, we investigate the dynamics of quantum Cournot duopoly game with heterogeneous players by using the Li et al. scheme. Further, we discuss the effect of quantum entanglement on local stability of the system. The results show that: (i) The special form of quantum Cournot duopoly game is the classical Cournot duopoly game, and the quantum Cournot duopoly game with naïve expectation is also a special form of quantum Cournot duopoly game with adaptive expectation. (ii) The increase or decrease of the stable region is dependent on the degree of quantum entanglement. It is related to the difference of relative marginal cost. (iii) The numerical simulation reveals the complexity characteristics of quantum dynamic Cournot game system through the analysis of stability region, bifurcation, strange attractor and sensitivity to initial conditions, and shows the difference from the classical dynamic Cournot model.

Effect of Induced Transition on the Quantum Entanglement and Coherence in Two‐Coupled Double Quantum Dot System

AbstractStudying quantum properties in solid‐state systems is a significant avenue for research. In this scenario, double quantum dots appear as a versatile platform for technological breakthroughs in quantum computation and nanotechnology. This work inspects the thermal entanglement and quantum coherence in two‐coupled DODs, where the system is exposed to an external stimulus that induces an electronic transition within each subsystem. The results show that the introduction of external stimulus induces a quantum level crossing that relies upon the Coulomb potential changing the degree of quantum entanglement and coherence of the system. Thus, the quantum properties of the system can be tuned by changing the transition frequency, leading to the enhancement of its quantum properties.

Pairwise entanglement in a three-cavity optomechanical system

Understanding the behavior of quantum entanglement in a multipartite quantum system has deep applications in quantum communication. Here, we study the pairwise entanglement between mechanical modes in an optomechanical system consisting of three distant Fabry-Pérot cavities driven by three independent coherent lasers and mutually fed by two-mode squeezed light. We observe that the degree of quantum entanglement, quantified by means of the logarithmic negativity, between any two mechanical modes increases by enhancing the squeezing parameter characterizing the two-mode squeezed light feeding the two corresponding cavities. On the other hand, we show that increasing the irrelevant squeezing parameters reduces the considered pairwise entanglement. In this way, one can control the pairwise entanglement in the optomechanical system by properly manipulating the squeezing parameters. Moreover, the optimal amount of entanglement is obtained for equal optomechanical couplings.

Entanglement degree of high-dimensional quantum low-density parity check codes

The important part of quantum information science is quantum error-correction and quantum computation. In thepractical application, some methods of quantum communication, such as the quantum communication based on the atmosphere transmission, require a mix ofmathematics-potentially to solve the problem. The quantum error-correction code is an efficient method to calculate quantum communication. However,since the construction of quantum error-correction codes depends on the degree of quantum entanglement, it is difficult to be widely used in practice.At present, the graph state is a promising solution to reduce the degree of codewords entanglement. But there are still many difficulties in constructingthe high-dimensional graph state. More importantly, the above difficulties can be skillfully solved by the upper and lower bounds of codewords entanglement.Based on the characteristics of the cyclic difference set of stabilizer codes and the combination of U and B of classical low-density parity check (LDPC) codes,a high-dimensional quantum low-density parity check (QLDPC) code is constructed creatively. By calculating the characteristics of the non-$Z$-type generators ofthe new codewords, the minimum number is obtained and the entanglement upper bound of the new code is acquired. And then, the rank of the check matrix of thenew code is calculated as the lower bound of entanglement. When the upper bound and lower bound of entanglement are different, the learning vectorquantization (LVQ) algorithm in machine learning can be used to simultaneously obtain the codewords entanglement and the coding complexity of the code,in which the relationship between them can be derived. In terms of calculating the running speed, compared with the iterative algorithm in the Lagrange multipliermethod, the running speed of LVQ algorithm is increased by $37.68%$. In this paper, a measurement of quantum codewords entanglement is proposed, which supports a helpful role in thedesign of quantum error-correction codes with higher decoding efficiency.

Biphoton topology in a quadratic nonlinear waveguide array under the Su-Schrieffer-Heeger model

We demonstrate the generation of a stable topologically nontrivial biphoton state with a high degree of quantum entanglement by the bosonic Bogoliubov Hamiltonian in a quadratic nonlinear waveguide array (QNWA) under the Su-Schrieffer-Heeger model. Analysis of its energy spectrum and eigenmode spectra verifies that this biphoton state is a topological nontrivial edge state characterized by the nonzero Berry phase at 1/4 and 3/4 fillings. The changes of Berry phase at 1/4 and 3/4 fillings indicate the topological quantum transition. The topological robustness of the biphoton edge state can be demonstrated by the spatial correlation under random disorders in propagation constant of the QNWA. It is also shown that the R\'enyi entanglement entropy of this topologically nontrivial biphoton state can approach high values. The robustness of this topologically nontrivial property suggests the promising application of this highly entangled biphoton state in quantum computing and information.

Quantum Cournot duopoly game with isoelastic demand function

This paper studies the quantum Cournot duopoly games with isoelastic demand function and unequal marginal costs by using the Li–Du–Massar and the Frąckiewicz quantum schemes. The influences of relative marginal cost and degree of quantum entanglement on the optimal profits of the two players are analyzed theoretically and illustrated numerically. The results show that the profit of one player increase, but the profit of the other player decreases with increasing the relative marginal cost for any fixed degree of quantum entanglement. The profits of two players both increase with increasing the degree of quantum entanglement as the relative marginal cost is in a certain range.

Quantum Stackelberg duopoly game with isoelastic demand function

We apply Frąckiewicz's scheme to investigate a quantum Stackelberg duopoly game with isoelastic demand function and unequal marginal costs. We analyze the existence conditions of quantum equilibrium, and the influences of relative marginal cost (m) and degree of quantum entanglement (γ) on the optimal profits and the first-mover advantage in theory. We demonstrate the theoretical analysis by numerical simulations. The results show that an increase of m will increase one player's profit, but will decrease the other player's profit for any fixed γ. An increase of γ will increase both players' profits for any fixed m. An increase of γ will enhance the first-mover advantage for 0<m<1, but will suppress it for 1<m<2.

Quantum entanglement and teleportation in superposition of multiple-photon-added two-mode squeezed vacuum state

In this paper, a new state called superposition of multiple-photon-added two-mode squeezed vacuum state (SMPA-TMSVS) is introduced by adding the multiple photons to both modes of a two-mode squeezed vacuum state (TMSVS). We explicitly investigate the degree of quantum entanglement, the Einstein–Podolsky–Rosen (EPR) correlation and the quantum steering in the SMPA-TMSVS. The results show in the SMPA-TMSVS that the degree of entanglement and the EPR correlation can be enhanced by nonlocal adding photons to a TMSVS. The quantum steering appears in the SMPA-TMSVS in case the superposition of single-photon addition [Formula: see text], in which mode [Formula: see text] can steer mode [Formula: see text]. By using the SMPA-TMSVS as an entangled resource, the quantum teleportation process is studied in detail based on the Vaidman–Braunstein–Kimble (VBK) protocol.

IN THE CONTEXT OF TIME-INDEPENDENT PARAMETERS IN TWO QUANTUM SYSTEMS: QUANTUM ENTANGLEMENT AND CORRELATIONS WITH NEGATIVITY MEASUREMENT

In this paper, we consider two phonons and three-level trapped ion in configuration forming Hilbert 12-space. The negativity and quantum correlations are revealed in trapped ion two phonon states system. Three values of LDP, = 0.006, =0.06 and =0.08 are given. The effects of the time-independent coupling in terms of the system, degree of quantum entanglement are investigated. Therefore, we have found the main optimal times for obtaining the high amount of entanglement with negativity.In this paper, we consider two phonons and three-level trapped ion in configuration forming Hilbert 12-space. The negativity and quantum correlations are revealed in trapped ion two phonon states system. Three values of LDP, = 0.006, =0.06 and =0.08 are given. The effects of the time-independent coupling in terms of the system, degree of quantum entanglement are investigated. Therefore, we have found the main optimal times for obtaining the high amount of entanglement with negativity.

Quantum entanglement and violation of Bell’s inequality in dipolar interaction system under Dzyaloshinsky–Moriya interaction

The Dzyaloshinsky–Moriya (DM) interaction contributes to some unusual and interesting magnetic properties in real materials, thus playing an important role in the degree of quantum entanglement in Heisenberg quantum spin models. In [C. S. Castro, O. S. Duarte, D. P. Pires, D. O. Soares-Pinto and M. S. Reis, Phys. Lett. A 380, 1571 (2016)], it has been investigated about the non-locality and the thermal entanglement in a dipolar spin thermal system without DM interaction. In this work, we study the entanglement in the thermal state of inhomogeneous Heisenberg coupling under the presence of the DM interaction along the [Formula: see text]-axis. More precisely, we analyze the effect of the DM interaction on non-locality phenomena and quantum entanglement as measured by negativity and Von Neumann entropy. We show that by comparing with [C. S. Castro, O. S. Duarte, D. P. Pires, D. O. Soares-Pinto and M. S. Reis, Phys. Lett. A 380, 1571 (2016)], the local quantum states become more pronounced, when the DM interaction is taken into account. This fact is well confirmed by noting that Von Neumann entropy is destroyed in the presence of the DM interaction. It can be deduced that the Dzyaloshinsky–Moriya (DM) interaction makes the thermal states less correlated.

Entangled Pair of the su(1) Quantum Systems Interacting with Two Two-Level Atoms

In this communication, we consider a pair of entangled quantum systems, each described by the su(1) Lie algebra, interacting with two two-level atoms. We discuss in detail the influence of the detuning terms on the system and derive from the Heisenberg equations of motion the expressions of various operators corresponding to the dynamics. Solving the associated Schrodinger equation, we obtain the general solution. Then we calculate and discuss in detail the expression of the von Neumann entropy for the two qubits and the radiation field. We examine the negativity index to gauge the degree of quantum entanglement between the su(1) quantum system and the atoms. Finally, we compare the results of the negativity and von Neumann entropy for some values of the initial state and the detuning parameter.

Counterpropagating continuous-variable entangled states in lossy coupled-cavity optical waveguides

We present an integrated source of counterpropagating entangled states based on a coupled resonator optical waveguide that is pumped by a classical pulsed source incident from above the waveguide. We investigate theoretically the generation and propagation of continuous variable entangled states in this coupled-cavity system in the presence of intrinsic loss. Using a tight-binding approximation, we derive analytic time-dependent expressions for the number of photons in each cavity, as well as for the correlation variance between the photons in different pairs of cavities, to evaluate the degree of quantum entanglement. We also derive simple approximate expressions for these quantities that can be used to guide the design of such systems, and discuss how pumping configurations and physical properties of the system affect the photon statistics and the degree of quantum correlation.

Quantum Fuzzy Game Simulation

This article studies quantum games with imprecise payoffs simulated by means of fuzzy numbers. Three two-person game-types are scrutinized via the iterated confronting of a large number of players laying in a two-dimensional lattice. In every iteration, every player interacts with his nearest neighbours and adopts the strategy of his best paid mate. Variable degree of quantum entanglement and of optimism in the fuzzy payoffs are taken into consideration in the study.

Simulation of the quantum Cournot duopoly game

This article studies the quantum Cournot duopoly game via the iterated confronting of a large number of players laying in a two-dimensional lattice. In every iteration, every player plays with his nearest partners and adopts the strategy of his best paid nearest mate. Variable degree of quantum entanglement is taken into consideration in the study.

Nonlinear dynamics of a quantum Cournot duopoly game with heterogeneous players

In this paper, a dynamic quantum Cournot duopoly game with heterogeneous players is proposed by applying the Li–Du–Massar scheme. We analyze the influence of the degree of quantum entanglement (DQE) on stability and dynamics behavior of the system. The result shows that: (i) The corresponding classical Cournot duopoly game is a special case of the dynamic quantum Cournot duopoly game. (ii) The stability region may increase or decrease as the DQE increases. It depends on the relative marginal cost difference. (iii) Numerical simulations show that the complicated dynamics behaviors of quantum Cournot game is different from that of corresponding classical model.

Magnetization processes and quantum entanglement in a spin-1/2 Ising-Heisenberg chain model of a heterotrimetallic Fe-Mn-Cu coordination polymer

Abstract We introduce and exactly solve a spin-1/2 Ising-Heisenberg chain that captures some relevant aspects of the heterotrimetallic coordination compound [ Cu II Mn II ( L 1 )] [ Fe III (bpb)(CN)2] · ClO 4 · H 2 O to be further abbreviated as Fe-Mn-Cu. The magnetic backbone of the coordination polymer Fe-Mn-Cu forms a regular alternation of Fe3+ and Mn2+ ions, whereas Cu 2 + ions are laterally attached to Mn2+ ions. The exchange coupling between Fe3+and Mn2+ ions is assumed to be Ising-like, while the exchange coupling between Cu 2 + and Mn2+ ions is assumed to be an anisotropic XXZ Heisenberg interaction. The gyromagnetic factors of all three metal ions are adjusted so as to obtain proper magnetic moment of individual metal ions when they are treated as spin-1/2 carriers. The ground-state phase diagram exhibits four distinct phases, whereas two of them display a quantum entanglement between spin states of Cu 2 + and Mn2+ ions. It is shown that the magnetization continuously varies with the magnetic field within two quantum ground states due to the mismatch between the magnetic moments and it also exhibits interesting field-driven phase transitions. The degree of quantum entanglement between the spin states of Cu 2 + and Mn2+ ions is quantified by the concurrence, which unveils that the entanglement becomes optimal at finite magnetic fields within one of the quantum ground states. The concurrence may exhibit non-monotonous dependences on the magnetic field and temperature.

Phase diagram and re-entrant fermionic entanglement in a hybrid Ising-Hubbard ladder.

The degree of fermionic entanglement is examined in an exactly solvable Ising-Hubbard ladder, which involves interacting electrons on the ladder's rungs described by Hubbard dimers at half-filling on each rung, accounting for intrarung hopping and Coulomb terms. The coupling between neighboring Hubbard dimers is assumed to have an Ising-like nature. The ground-state phase diagram consists of four distinct regions corresponding to the saturated paramagnetic, the classical antiferromagnetic, the quantum antiferromagnetic, and the mixed classical-quantum phase. We have exactly computed the fermionic concurrence, which measures the degree of quantum entanglement between the pair of electrons on the ladder rungs. The effects of the hopping amplitude, the Coulomb term, temperature, and magnetic fields on the fermionic entanglement are explored in detail. It is shown that the fermionic concurrence displays a re-entrant behavior when quantum entanglement is being generated at moderate temperatures above the classical saturated paramagnetic ground state.