Entropic entanglement criteria for Fermion systems

Entanglement criteria for general (pure or mixed) states of systems consisting of two identical fermions are introduced. These criteria are based on appropriate inequalities involving the entropy of the global density matrix describing the total system, on the one hand, and the entropy of the one-particle reduced density matrix, on the other hand. A majorization-related relation between these two density matrices is obtained, leading to a family of entanglement criteria based on Rényi’s entropic measure. These criteria are applied to various illustrative examples of parametrized families of mixed states. The dependence of the entanglement detection efficiency on Rényi’s entropic parameter is investigated. The extension of these criteria to systems of N identical fermions is also considered.     

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     

Entropy product measure for multipartite pure states

An entanglement measure for multipartite pure states is formulated using the product of the von Neumann entropy of the reduced density matrices of the constituents. Based on this new measure, all possible ways of the maximal entanglement of the triqubit pure states are studied in detail and all types of the maximal entanglement have been compared with the result of ‘the average entropy’. The new measure can be used to calculate the degree of entanglement, and an improvement is given in the area near the zero entropy.     

Simple Entanglement Measure for Multipartite Pure States

A simple entanglement measure for multipartite pure states is formulated based on the partial entropy of a series of reduced density matrices. Use of the proposed new measure to distinguish disentangled, partially entangled, and maximally entangled multipartite pure states is illustrated.     

Sufficient and Necessary Conditions of Entanglement Transformations Between Mixed States

Based on a new measure of entanglement for finite-dimensional bi-particle pure states, we give sufficient and necessary conditions that a bi-particle mixed state ρ can be transformed into another mixed state σ by local operations and classical communication (LOCC). This result can be regarded as a generalization of Nielsen’s theorem (Nielsen, Phys. Rev. Lett. 83:436, 1999). However, we find that it is more difficult to determine the entanglement transformations between mixed states than to do between pure ones.     

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 in four qubit states: Polynomial invariant of degree 2, genuine multipartite concurrence and one-tangle

Characterization of the multipartite mixed state entanglement is still a challenging problem. This is due to the fact that the entanglement for the mixed states, in general, is defined by a convex-roof extension. That is the entanglement measure of a mixed state ρ of a quantum system can be defined as the minimum average entanglement of an ensemble of pure states. In this paper, we show that polynomial entanglement measures of degree 2 of even-N qubits X states is in the full agreement with the genuine multipartite (GM) concurrence. Then, we plot the hierarchy of entanglement classification for four qubit pure states and then using new invariants, we classify the four qubit pure states. We focus on the convex combination of the classes whose at most the one of the invariants is non-zero and find the relationship between entanglement measures consist of non-zero-invariant, GM concurrence and one-tangle. We show that in many entanglement classes of four qubit states, GM concurrence is equal to the square root of one-tangle.     

Dynamical entanglement for Fermi coupled stretching and bending modes

The dynamical entanglement for Fermi coupled C--H stretch and bend vibrations in molecule CHD₃ is studied in terms of two negativities and the reduced von Neumann entropy, where initial states are taken to be direct products of photon-added coherent states on each mode. It is demonstrated that the negativity defined by the sum of negative eigenvalues of the partial transpose of density matrices is positively correlated with the von Neumann entropy. The entanglement difference between photon-added coherent states and usual coherent states is discussed as well.     

Complementarity Relations for Multi-Qubit Systems

No Heading We derive two complementarity relations that constrain the individual and bipartite properties that may simultaneously exist in a multi-qubit system. The first expression, valid for an arbitrary pure state of n qubits, demonstrates that the degree to which single particle properties are possessed by an individual member of the system is limited by the bipartite entanglement that exists between that qubit and the remainder of the system. This result implies that the phenomenon of entanglement sharing is one specific consequence of complementarity. The second expression, which holds for an arbitrary state of two qubits, pure or mixed, quantifies a tradeoff between the amounts of entanglement, separable uncertainty, and single particle properties that are encoded in the quantum state. The separable uncertainty is a natural measure of our ignorance about the properties possessed by individual subsystems, and may be used to completely characterize the relationship between entanglement and mixedness in two-qubit systems. The two-qubit complementarity relation yields a useful geometric picture in which the root mean square values of local subsystem properties act like coordinates in the space of density matrices, and suggests possible insights into the problem of interpreting quantum mechanics.     

Effect of Intrinsic Decoherence of Milburn＇s Model on Entanglement of Two-Qutrit States

We analyze the time evolution of entanglement of two-qutrit system within the framework of Milburn's model of intrinsic decoherence. The entanglement evolution relies not only on the parameters of system, but also on the concrete states either pure or mixed. The linear entropy used to measure the extent to which the intrinsic decoherence affects quantum states is evaluated.     

Complementary relation between quantum entanglement and entropic uncertainty

Quantum entanglement is regarded as one of the core concepts,which is used to describe the nonclassical correlation between subsystems,and entropic uncertainty relation plays a vital role in quantum precision measurement.It is well known that entanglement of formation can be expressed by von Neumann entropy of subsystems for arbitrary pure states.An interesting question is naturally raised:is there any intrinsic correlation between the entropic uncertainty relation and quantum entanglement?Or if the relation can be applied to estimate the entanglement.In this work,we focus on exploring the complementary relation between quantum entanglement and the entropic uncertainty relation.The results show that there exists an inequality relation between both of them for an arbitrary two-qubit system,and specifically the larger uncertainty will induce the weaker entanglement of the probed system,and vice versa.Besides,we use randomly generated states as illustrations to verify our results.Therefore,we claim that our observations might offer and support the validity of using the entropy uncertainty relation to estimate quantum entanglement.     

Entanglement and statistical independence for mixed quantum states

We show that three conditions associated with “entanglement,”viz., non-locality, non-factorisability and statistical dependence, are equivalent for pure states, and that non-factorisability and statistical dependence are equivalent for mixed states. Discussion then reinforces the generally held view that the key condition for mixed states is nonseparability.     

Control of purity and entanglement for two spatially two-separated qubits via phase damping

Control of purity and entanglement of two two-qubits dispersively coupled to a field with a reservoir are investigated.Initially the qubits are entangled,while the field is either in a coherent state or a statistical mixture of two coherent states.For an alternative entanglement measure we calculate the negativity of the eigenvalues of the partially transposed density matrix.A measure related to the mutual entropy,namely the index of entropy,is employed to measure the entanglement.Its results agree well with the negativity.It is found that the entanglement and purity have strong sensitivity to phase damping.The asymptotic behaviour of the states of the field,the two two-qubits,and the total system fall into mixed states.     

Entanglement capacity of two-qubit unitary operator for rank two mixed states

The entanglement capacity of two-qubit unitary operator acting on rank two mixed states in concurrence is discussed. The condition of perfect entangler is the same as that acting on pure states and the entanglement capacity is the mixing parameter v1. For non-perfect entangler, the upper and lower bound of the entanglement capacity are given.     

Monogamy Relations in Terms of Tsallis-Q Entropy in any Dimensional System

Monogamy of entanglement is a fundamental property of multipartite entangled states. In this article, due to the convexity of Trρ^q with respect to q when q ≥ 1, we give a monogamy-like relation in terms of Tsallis-q entanglement entropy of assistance (TqEEA) for pure states over an n- partite any dimensional system and monogamy-like relations in terms of Tsallis-q entanglement entropy (TqEE) for mixed states for any dimensional system, we also give a lower bound for the TqEE of a four-partite pure state. At last, we show that the generalized W-class states satisfy the polygamy relation in terms of TqEE when q = 2.     

Dynamical correlations of negativity and entropy for pure and mixed states in two coupled quartic oscillators

Various measures of entanglement have triggered considerable interest in the relationship between entanglement measures and other well-known quantities. As a demonstration, the dynamical correlation of negativity and entropy is studied in two coupled quartic oscillators for initial pure and mixed states that are respectively taken to be the products and mixed density matrices of coherent states and squeezed states on each oscillator. The correlation with energy is also considered. It is shown that for the initial pure states with a small magnitude, two negativities are positively correlated with the von Neumann entropy while they are anti-correlated with the energy of each oscillator in the weak coupling regime. For mixed states with a small magnitude the two negativities and the mutual entropy exhibit dominantly positive correlation, whereas those three quantities are dominantly anti-correlated with the sum of energies of two oscillators in the case of weak interactions. Such correlation behaviors in the mixed state with small magnitudes are most striking at the same step in maximal and minimal values and in oscillation. The differences in entropies and negativities between coherent states and squeezed states are discussed. These are useful for quantum entanglement and quantum information processing.     

Free entanglement measure of multiparticle quantum states

In this Letter, based on the classification of multiparticle states and the original definition of semiseparability, we give out the redefinition of semiseparability and inseparability of multiparticle states. By virtue of the redefinition, entanglement measure of multiparticle states can be converted into bipartite entanglement measure in arbitrary dimension in mathematical method. A simple expression of entanglement measure is given out. As examples, a general three-particle pure state and an N-particle mixed state are considered.     

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.     

原子与双模相干强场依赖强度耦合多光子过程中纠缠量度与制备

给出了依赖强度耦合双模多光子过程Jaynes-Cummings模型的有效哈密顿量.在强场条件下,分别用量子约化熵和量子相对熵研究了上述模型中原子与场之间的纠缠以及双模相干场的模间纠缠演化.研究表明,这两类纠缠演化均与原子跃迁时吸收(或发射)的光子数k密切相关.同时,还揭示了双光子过程(k=1)和多光子过程(k≥2)中不同的纠缠特性.讨论了纠缠态的制备,制备了与时间无关的原子-场的Einstein-Podolsky-Rosen态和双模相干场的模间纠缠态.     

三体纯态的纠缠度与量子控制隐形传送的理论分析

对三体纯态,V.Coffman等提出了分布纠缠的概念及纠缠的度量"tangle".本文由变换算符出发,以三粒子作为量子通道对一个任意的粒子态实现控制隐形传送为例,给出纠缠度与量子控制隐形传态之间满足的关系.