Entanglement property in matrix product spin systems

We study the entanglement property in matrix product spin-ring systems systemically by von Neumann entropy. We find that: (i) the Hilbert space dimension of one spin determines the upper limit of the maximal value of the entanglement entropy of one spin, while for multiparticle entanglement entropy, the upper limit of the maximal value depends on the dimension of the representation matrices. Based on the theory, we can realize the maximum of the entanglement entropy of any spin block by choosing the appropriate control parameter values. (ii) When the entanglement entropy of one spin takes its maximal value, the entanglement entropy of an asymptotically large spin block, i.e. the renormalization group fixed point, is not likely to take its maximal value, and so only the entanglement entropy Sn of a spin block that varies with size n can fully characterize the spin-ring entanglement feature. Finally, we give the entanglement dynamics, i.e. the Hamiltonian of the matrix product system.     

The entanglement property in matrix product spin systems

We study the entanglement property in matrix product spin-ring systems systemically by von Neumann entropy. We nd that: (i) the Hilbert space dimension of one spin determines the upper limit of the maximal value of the entanglement entropy of one spin, while for multiparticle entanglement entropy, the upper limit of the maximal value depends on the dimension of the representation matrices. Based on the theory, we can realize the maximum of the entanglement entropy of any spin block by choosing the appropriate control parameter values. (ii) When the entanglement entropy of one spin takes its maximal value, the entanglement entropy of an asymptotically large spin block, i.e. the renormalization group fixed point, is not likely to take its maximal value, and so only the entanglement entropy S_n of a spin block that varies with size n can fully characterize the spin-ring entanglement feature. Finally, we give the entanglement dynamics, i.e. the Hamiltonian of the matrix product system.     

Relative entropy as a measure of entanglement for Gaussian states

In this paper, we derive an explicit analytic expression of the relative entropy between two general Gaussian states. In the restriction of the set for Gaussian states and with the help of relative entropy formula and Peres--Simon separability criterion, one can conveniently obtain the relative entropy entanglement for Gaussian states. As an example, the relative entanglement for a two-mode squeezed thermal state has been obtained.     

Entropy and Entanglement of the Electromagnetically Induced Transparency System

We study the entropy and the entanglement of an electromagnetically induced transparency system. The quantumentanglement between the atom and the two quantized laser fields is discussed by using quantum reduced entropyand that between the two quantized laser fields by using quantum relative entropy. We also examine whetherinfluences of EIT on entropy and quantum entanglement of the system considered occur or not. Our resultsshow that the minimum value of the atomic reduced entropy may be regarded as an entropy criterion on theelectromagnetically induced transparency occurring.     

Properties of Linear Entropy in k-Photon Jaynes-Cummings Model with Stark Shift and Kerr-Like Medium

The time evolution of the linear entropy of an taking into consideration Stark shift and Kerr-like medium. atom in k-photon daynes-Cummings model is investigated The effect of both the Stark shift and Kerr-like medium on the linear entropy is analyzed using a numerical technique for the field initially in coherent state and in even coherent state. The results show that the presence of the Kerr-like medium and Stark shift has an important effect on the properties of the entropy and entanglement. It is also shown that the setting of the initial state plays a significant role in the evolution of the linear entropy and entanglement.     

Entanglement of Generalized Two-Mode Binomial States and Teleportation

The entanglement of the generalized two-mode binomial states in the phase damping channel is studied by making use of the relative entropy of the entanglement. It is shown that the factors of q and p play the crucial roles in control the relative entropy of the entanglement. Furthermore, we propose a scheme of teleporting an unknown state via the generalized two-mode binomial states, and calculate the mean fidelity of the scheme.     

Quantum entanglement in the mode-mode competition system

Considering a two-level atom interacting with the competing two-mode field, this paper investigates the entanglement between the two-level atom and the two-mode field by using the quantum reduced entropy, and that between the two-mode field by using the quantum relative entropy of entanglement. It shows that the two kinds of entanglement are dependent on the relative coupling strength of atom-field and the atomic distribution, and exhibit the periodical evolution. The maximal atom-field entanglement state can be prepared via the appropriate selection of system parameters and interaction time.     

Structure formation of entanglement entropy in a system of two superconducting qubits coupled with an LC-resonator

This paper investigates theoretically the evolutions of the entanglement entropy of a system of two coupled-charge-qubits interacting with an LC-resonator.It is found that when the initial states of the two qubits are prepared in a given superposition excited state,the evolution of the von Neumann entropy of the system depends significantly on the coupling strength between the two Josephson charge qubits.With the variation of the coupling strength,the evolution of the entanglement entropy of the system forms some structures,especially the periodically bistable properties,which are the first discovered for such a system to our knowledge.It is found that the relative entropy entanglement of the system is also sensitive to the variation of the coupling strength between the two charge qubits,some novel ’collective oscillations’ of the relative entropy are found for the system.     

Quantum entanglement between the two-mode fields and atomic entropy squeezing in the system of a moving atom interacting with two-mode entangled coherent field

This paper investigates the entropy squeezing of a moving two-level atom interacting with the two-mode entangled coherent field via two-photon transition by using an entropic uncertainty relation and the degree of entanglement between the two-mode fields by using quantum relative entropy. The results obtained from numerical calculation indicate that the squeezed period, the duration of entropy squeezing and the maximal squeezing can be controlled by appropriately choosing the intensity of the light field, the atomic motion and the field-mode structure. The atomic motion leads to the periodic recovery of the initial maximal degree of entanglement between the two-mode fields. Moreover, there exists a corresponding relation between the time evolution properties of the atomic entropy squeezing and those of the entanglement between the two-mode fields.     

Partial entropy change and entanglement in the mixed state for a Jaynes－Cummings model with Kerr medium

By using the algebraic dynamical approach, an atom--field bipartite system in mixed state is employed to investigate the partial entropy change and the entanglement in a cavity filled with Kerr medium. The effects of different nonlinear intensities are studied. One can find that the Kerr nonlinearity can reduce the fluctuation amplitudes of the partial entropy changes and the entanglement of the two subsystems, and also influence their periodic evolution. Meanwhile, increasing the Kerr nonlinear strength can convert the anti-correlated behaviour of the partial entropy change to the positively correlated behaviour. Furthermore, the entanglement greatly depends on the temperature. When the temperature or the nonlinear intensity increases to a certain value, the entanglement can be suppressed greatly.     

负值量子条件熵与双量子系统一类混合态纠缠量度

运用负值量子条件熵研究了双量子系统一类混合态的纠缠量度.给出了负值量子条件作为条件熵纠缠度的定义，证明了条件熵纠缠满足作为2×2系统一类混合纠缠态量度的四个基本条件.当双量子系统处于纯态时，条件熵纠缠度即为部分熵纠缠度.应用条件熵纠缠度研究了真空腔场中两全同二能级原子之间纯态和一类混合态纠缠的时间演化，比较了相同条件下两全同原子系统concurrence纠缠度的时间演化.结果表明，两纠缠度演化规律完全一致，验证了负值量子条件熵可以作为双量子系统纯态和一类混合态的纠缠量度. 关键词： 双量子系统 负值量子条件熵 条件熵纠缠度 混合态纠缠度     

Entanglement Entropy in an Opened Antiferromagnetic Heisenberg Chain with Alternating Interaction

The effects of alternating interaction on the bipartite entanglement are considered in an antiferromagnetic Heisenberg opened chain. Entropy is used to evaluate bipartite entanglement in the system. There are large oscillations between even and odd L-values entropy. The even (odd)-values entropy increases when the length of the subsystem increases. The method of density matrix renormalization-group is applied to obtain logarithmic behavior of entropy.     

Entanglement Entropy Evolution under Double‐trace Deformation

In this paper, we study the bulk entanglement entropy evolution in conical BTZ black bole background using the heat kernel method. This is motivated by exploring the new examples where the quantum correction of the entanglement entropy gives the leading contribution. We find that in the large black hole limit the bulk entanglement entropy decreases under the double‐trace deformation which is consistent with the holographic c theorem and in the small black hole limit the bulk entanglement entropy increases under the deformation. We also discuss the minimal area correction.     

Entropy and Entanglement of a Single-mode Vacuum Field Interacting with a Ξ-type Three-level Atom with Detuning

The evolution of the field entropy and the entanglement between the atom and the field for the system of a single-mode vacuum field interacting with a Ξ-type three-level atom have been studied by using the reduced quantum entropy. The influences of the detuning of the light field and the setting of the initial state of the atom on the field entropy and entanglement of the system under consideration are discussed emphatically. It is showed that the detuning of the light field and the setting of the initial state of the atom play an important role for the evolution of the field entropy and the entanglement between the atom and the field. The general conclusions reached are illustrated by numerical results.     

k光子Jaynes-Cummings模型与运动原子相互作用中的熵交换及纠缠

文章研究了k光子Jaynes-Cummings模型与运动原子相互作用中的熵相互关系及纠缠特性.发现原子与光场之间具有熵交换特性.讨论了原子运动、光子数k和场模结构等因素对原子与光场熵相互关系的影响.此外,讨论了原子与场系统熵交换与纠缠之间的关系. 关键词： 熵交换 纠缠 Jaynes-Cummings模型 原子运动     

Numerical study of entanglement entropy in lattice gauge theory

The entropy of entanglement between a three-dimensional slab of thickness l and its complement is studied numerically for four-dimensional SU(2) lattice gauge theory. We find a signature of a nonanalytic behavior of the entanglement entropy, which was predicted recently for large N_c confining gauge theories in the framework of AdS/CFT correspondence. The derivative of the entanglement entropy over l is likely to have a discontinuity at some l=l_c. It is argued that such behavior persists even at finite temperatures, probably turning into a sort of crossover for temperatures larger than the temperature of the deconfinement phase transition. We also confirm that the entanglement entropy contains quadratically divergent l-independent term, and that the nondivergent terms behave as l⁻² at small distances.     

Kerr效应对非线性Jaynes-Cummings模型场熵和缠结的影响

Phoenix和Knight提出的量子熵理论,用量子熵作为缠结程度的量度,研究了附加克尔介质依赖强度耦合Jaynes-Cummings模型场熵演化的动力学特性和原子-场的缠结特性,详细地讨论了克尔效应及初始相干光场的强弱对场熵演化特性和原子-场缠结特性的影响,并与原子反转特性相比较.结果表明:在初始相干光场较弱时(n=10),克尔介质的非线性相互作用破坏了场熵演化的周期性,原子-场不再周期消缠结.但在初始相干光场较强时(n=50),克尔介质非线性相互作用只是使场熵演化的周期性减弱,场熵的演化仍近似地有周期性,原子-场仍周期消缠结,克尔效应越强,周期越小.当克尔介质与光场强耦合相互作用时(χ/g=5),原子-场持续消缠结.     

Entanglement of electronic subbands and coherent superposition of spin states in a Rashba nanoloop

The present work is concerned with an analysis of the entanglement between the electronic coherent superpositions of spin states and subbands in a quasi-one-dimensional Rashba nanoloop acted upon by a strong perpendicular magnetic field. We explicitly include the confining potential and the Rashba spin-orbit coupling into the Hamiltonian and then proceed to calculate the von Neumann entropy, a measure of entanglement, as a function of time. An analysis of the von Neumann entropy demonstrates that, as expected, the dynamics of entanglement strongly depends upon the initial state and electronic subband excitations. When the initial state is a pure one formed by a subband excitation and the z-component of spin states, the entanglement exhibits periodic oscillations with local minima (dips). On the other hand, when the initial state is formed by the subband states and a coherent superposition of spin states, the entanglement still periodically oscillates, exhibiting stronger correlations, along with elimination of the dips. Moreover, in the long run, the entanglement for the latter case undergoes the phenomenon of collapse-revivals. This behaviour is absent for the first case of the initial states. We also show that the degree of entanglement strongly depends upon the electronic subband excitations in both cases.     

费米环境中两个三能级原子系统的纠缠演化

利用负性纠缠度(negativity)研究了两个三能级原子系统在费米环境中的纠缠演化问题-结果表明,两个三能级原子系统的纠缠演化不仅依赖于系统和环境的相互作用强度,而且还依赖于系统所处的具体量子态-通过例子发现,系统和环境相互作用强度越大,纠缠衰减越快;对于纯态,仅当时间趋于无穷时纠缠才被完全破坏;对于混态,则在有限的时间内纠缠即被彻底破坏-通过一般的分析找到了一类免退相干的量子子空间-在这些子空间中,量子态不受环境的影响,故其纠缠不变-研究有助于理解费米环境造成的退相干对玻色系统纠缠的影响- 关键词： 费米环境 纠缠演化 两个三能级原子