A Genuine Multipartite Entanglement Measure Generated by the Parametrized Entanglement Measure

A genuine multipartite entanglement measure based on the geometric method is investigated in this paper. This measure has desirable properties for quantifying the genuine multipartite entanglement. A lower bound of the genuine multipartite entanglement measure derived with the fidelity-based method is then presented. The advantages of the measure proposed here with other measures are also presented. At last, examples are presented to show that the genuine entanglement measure has distinct entanglement ordering from other measures.     

Tavis-Cummings模型中的几何量子失协特性

采用几何量子失协的计算方法,通过改变两原子初始状态、腔内光子数和偶极-偶极相互作用强度,研究了Tavis-Cummings模型中的几何量子失协特性.结果表明:几何量子失协都是随时间周期性振荡的,选取适当的初态可以使两原子一直保持失协状态,增加腔内光子数和偶极相互作用对几何量子失协有积极的影响.     

Measures of genuine multipartite entanglement for graph states

Graph states are special multipartite entangled states that have been proven useful in a variety of quantum information tasks. We address the issue of characterizing and quantifying the genuine multipartite entanglement of graph states up to eight qubits. The entanglement measures used are the geometric measure, the relative entropy of entanglement, and the logarithmic robustness, have been proved to be equal for the genuine entanglement of a graph state. We provide upper and lower bounds as well as an iterative algorithm to determine the genuine multipartite entanglement.     

Detect genuine multipartite entanglement in the one-dimensional transverse-field Ising model

Recently Seevinck and Uffink argued that genuine multipartite entanglement (GME) had not been established in the experiments designed to confirm GME. In this paper, we use the Bell-type inequalities introduced by Seevinck and Svetlichny [M. Seevinck, G. Svetlichny, Phys. Rev. Lett. 89 (2002) 060401] to investigate the GME problem in the one-dimensional transverse-field Ising model. We show explicitly that the ground states of this model violate the inequality when the external transverse magnetic field is weak, which indicate that the ground states in this model with weak magnetic field are fully entangled. Since this model can be simulated with nuclear magnetic resonance, our results provide a fresh approach to experimental test of GME.     

Local Information as an Essential Factor for Quantum Entanglement

Quantum entanglement is not only a fundamental concept in quantum mechanics but also a special resource for many important quantum information processing tasks. An intuitive way to understand quantum entanglement is to analyze its geometric parameters which include local parameters and correlation parameters. The correlation parameters have been extensively studied while the role of local parameters have not been drawn attention. In this paper, we investigate the question how local parameters of a two-qubit system affect quantum entanglement in both quantitative and qualitative perspective. Firstly, we find that the concurrence, a measure of quantum entanglement, of a general two-qubit state is bounded by the norms of local vectors and correlations matrix. Then, we derive a sufficient condition for a two-qubit being separable in perspective of local parameters. Finally, we find that different local parameters could make a state with fixed correlation matrix separable, entangled or even more qualitatively entangled than the one with vanished local parameters.     

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.     

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.     

Evaluating the geometric measure of multiparticle entanglement

We present an analytical approach to evaluate the geometric measure of multiparticle entanglement for mixed quantum states. Our method allows the computation of this measure for a family of multiparticle states with a certain symmetry and delivers lower bounds on the measure for general states. It works for an arbitrary number of particles, for arbitrary classes of multiparticle entanglement, and can also be used to determine other entanglement measures.     

Multiple Entropy Measures for Multi-particle Pure Quantum State

We propose to use a set of averaged entropies, the multiple entropymeasures (MEMS), to partially quantify quantum entanglement ofmultipartite quantum state. The MEMS is vector-like with m=[N/2]components: [S₁, S₂,..., S_m], and the $i$-th component S_i is the geometric mean of i-qubits partial entropy of the system. The S_i measures how strong an arbitrary i qubits from the system are correlated with the rest of the system. It satisfies the conditions for a good entanglement measure. We have analyzed the entanglement properties of the GHZ-state, the W-states, and cluster-states under MEMS.     

两态和三态多体纯态的度量和分类

基于多体纯态纠缠的度量方法，研究了两态两体和三体以及三态两体纯态纠缠的分类和度量.结果表明，在随机局域操作与经典通信(SLOCC)等价的意义下，纯态的纠缠方式可用所定义纠缠度的不同极大值来表征.通过仔细的计算和分析发现，两态三体和三态两体纯态各有三种SLOCC不等价的基本纠缠方式.最后将三态两体纯态纠缠度的计算与新近提出的熵积纠缠度方案进行了比较，并进行了讨论. 关键词： 纯态纠缠 极值纠缠 随机局域操作和经典通信     

一维倾斜场伊辛模型中的纠缠特性

在一维倾斜场伊辛模型中, 利用并发度和Q测量函数分别对系统的两体纠缠和整体纠缠进行度量, 通过讨论系统中量子纠缠的动力学特性, 能够体现出系统的可积和不可积行为. 由系统基态的纠缠特性可以发现只要倾角不为零时, 系统的Q测量函数会随着磁场的增大而减少, 而用并发度刻画的系统的相变特性, 随着磁场倾角的增大发生了变化. 考虑系统的动力学行为发现, 在一维倾斜场伊辛模型中, 不可积性会抑制两体纠缠, 却促进系统整体纠缠生成. 关键词： 伊辛模型 不可积性 两体纠缠 整体纠缠     

Thermal entanglement and teleportation of a thermally mixed entangled state of a Heisenberg chain through a Werner state

The thermal entanglement and teleportation of a thermally mixed entangled state of a two-qubit Heisenberg XXX chain under the Dzyaloshinski Moriya （DM） anisotropic antisymmetric interaction through a noisy quantum channel given by a Werner state is investigated. The dependences of the thermal entanglement of the teleported state on the DM coupling constant, the temperature and the entanglement of tbe noisy quantum channel are studied }n detail for both the ferromagnetic and the antiferromagnetic cases. The result shows that a minimum entanglement of the noisy quantum channel must be provided in order to realize the entanglement teleportation. The values of fidelity of the teleported state are also studied for these two cases. It is found that under certain conditions, we can transfer an initial state with a better fidelity than that for any classical communication protocol.     

Entanglement Evolution of Three-Qubit States under Local Decoherence

By using negativity as entanglement measure, we have investigated the effect of local decoherence from a non-Markovian environmenton the time evolution of entanglement of three-qubit states including the GHZ state, the W state, and the Werner state. From the results, we find that the entanglement dynamics depends not only on the coupling strengths but also on the specific states of concern. Specifically, the entanglement takes different behaviors under weak or strong coupling and it varies with the quantum states under study. The entanglement of the GHZ state and the Werner state can be destroyed completely by the local decoherence, while the entanglement of the W state can survive through the local decoherence partially.     

耦合系数对Tavis-Cummings模型中三体纠缠态纠缠量的影响

研究了两个全同二能级原子与单模场相互作用的Tavis-Cummings模型中的量子纠缠.在两原子初始时处于基态,光场处于单光子状态下,得出体系状态演化为近似W纠缠态.结果表明:两原子耦合量越大,三体纠缠态中两两纠缠量和三体纠缠量越小,其中两原子间纠缠量和三体纠缠量减小的程度更大,并且三体纠缠态中两两纠缠量和三体纠缠量的振荡周期也相应减小.     

Effect of spin-orbit interaction on entanglement of two-qutrit Heisenberg XYZ systems in an inhomogeneous magnetic field

We investigate the properties of spin-orbit interaction in the ground state and thermal entanglement of a two-qutrit Heisenberg XYZ system in the presence of an inhomogeneous magnetic field. Using negativity as entanglement measure, we give the dependence of entanglement on each parameter in detail. The result shows that one can get appropriate entanglement by adjusting the magnetic field, Dzyaloshinskii-Moriya interaction and anisotropy parameter simultaneously.     

Entanglement witnesses and geometry of entanglement of two-qutrit states

We construct entanglement witnesses with regard to the geometric structure of the Hilbert-Schmidt space and investigate the geometry of entanglement. In particular, for a two-parameter family of two-qutrit states that are part of the magic simplex, we calculate the Hilbert-Schmidt measure of entanglement. We present a method to detect bound entanglement which is illustrated for a three-parameter family of states. In this way, we discover new regions of bound entangled states. Furthermore, we outline how to use our method to distinguish entangled from separable states.     

Effect of spin-orbit interaction on entanglement of two-qutrit Heisenberg XYZ systems in an inhomogeneous magnetic field

We investigate the properties of spin-orbit interaction in the ground state and thermal entanglement of a two-qutrit Heisenberg XYZ system in the presence of an inhomogeneous magnetic field. Using negativity as entanglement measure, we give the dependence of entanglement on each parameter in detail. The result shows that one can get appropriate entanglement by adjusting the magnetic field, Dzyaloshinskii-Moriya interaction and anisotropy parameter simultaneously.     

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 Dynamics of Two-Qubit System in Different Types of Noisy Channels

In this paper, we study entanglement dynamics of a two-qubit extended Werner-like state locally, interacting with independent noisy channels, i.e., amplitude damping, phase damping, and depolarizing channels. We show that the purity of initial entangled state has direct impacts on the entanglement robustness in each noisy channel. That is, if the initial entangled state is prepared in mixed instead of pure form, the state may exhibit entanglement sudden death （ESD） and/or be decreased for the critical probability at which the entanglement disappear.