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.     

Separability criteria for multipartite quantum mixed states

The separability of mixed states in multipartite quantum systems is investigated. If a quantum state in a multipartite system with an arbitrary dimension is separable, some quantity in relation to Hermitian matrix is positive.     

Estimation of concurrence for multipartite mixed states

We investigate the lower bound of concurrence for multipartite quantum mixed states. Analytical lower bounds are derived for some multipartite systems, by establishing functional relations between concurrence and the generalized partial transpositions.     

Tensor rank and stochastic entanglement catalysis for multipartite pure states

The tensor rank (also known as generalized Schmidt rank) of multipartite pure states plays an important role in the study of entanglement classifications and transformations. We employ powerful tools from the theory of homogeneous polynomials to investigate the tensor rank of symmetric states such as the tripartite state |W3>=1/√3(|100> + |010> + |001>) and its N-partite generalization |W(N)>. Previous tensor rank estimates are dramatically improved and we show that (i) three copies of |W3> have a rank of either 15 or 16, (ii) two copies of |W(N)> have a rank of 3N - 2, and (iii) n copies of |W(N)> have a rank of O(N). A remarkable consequence of these results is that certain multipartite transformations, impossible even probabilistically, can become possible when performed in multiple-copy bunches or when assisted by some catalyzing state. This effect is impossible for bipartite pure states.     

Optimal entanglement criterion for mixed quantum states

We develop a strong and computationally simple entanglement criterion. The criterion is based on an elementary positive map Phi which operates on state spaces with even dimension N > or = 4. It is shown that Phi detects many entangled states with a positive partial transposition (PPT) and that it leads to a class of optimal entanglement witnesses. This implies that there are no other witnesses which can detect more entangled PPT states. The map Phi yields a systematic method for the explicit construction of high-dimensional manifolds of bound entangled states.     

Catalysis of entanglement manipulation for mixed states

We consider entanglement-assisted remote quantum state manipulation of bipartite mixed states. Several aspects are addressed: we present a class of mixed states of rank two that can be transformed into another class of mixed states under entanglement-assisted local operations with classical communication, but for which such a transformation is impossible without assistance. Furthermore, we demonstrate enhancement of the efficiency of purification protocols with the help of entanglement-assisted operations. Finally, transformations from one mixed state to mixed target states which are sufficiently close to the source state are contrasted with similar transformations in the pure-state case.     

多粒子纠缠的保护方案

量子纠缠是量子信息的重要物理资源. 然而当量子系统与环境相互作用时, 会不可避免地产生消相干导致纠缠下降, 因此保护纠缠不受环境的影响具有重要意义. 振幅衰减是一种典型的衰减机制. 如果探测环境保证没有激发从系统中流出, 即视为对系统的一种弱测量. 本文基于局域脉冲序列和弱测量, 提出了一种可以保护多粒子纠缠不受振幅衰减影响的有效物理方案, 保护的对象是在量子通信和量子计算中发挥重要作用的Cluster态和Maximal slice态.     

Operational interpretation for global multipartite entanglement

We introduce an operational interpretation for pure-state global multipartite entanglement based on quantum estimation. We show that the estimation of the strength of low-noise locally depolarizing channels, as quantified by the regularized quantum Fisher information, is directly related to the Meyer-Wallach multipartite entanglement measure. Using channels that depolarize across different partitions, we obtain related multipartite entanglement measures. We show that this measure is the sum of expectation values of local observables on two copies of the state.     

Decoherence and multipartite entanglement

We study the dynamics of multipartite entanglement under the influence of decoherence. A suitable generalization of concurrence reveals distinct scaling of the entanglement decay rate of Greenberger-Horne-Zeilinger and W states, for various environments.     

Comparability of multipartite entanglement

We prove, in a multipartite setting, that it is always feasible to exactly transform a genuinely m-partite entangled pure state with sufficient many copies to any other m-partite state via local quantum operation and classical communication. This result affirms the comparability of multipartite entangled pure states.     

Purified discord and multipartite entanglement

We study bipartite quantum discord as a manifestation of a multipartite entanglement structure in the tripartite purified system. In particular, we find that bipartite quantum discord requires the presence of both bipartite and tripartite entanglement in the purification. This allows one to understand the asymmetry of quantum discord, D(A,B)≠D(B,A)$D(A,B)\ne D(B,A)$ in terms of entanglement monogamy. As instructive special cases, we study discord for qubits and Gaussian states in detail. As a result of this we shed new light on a counterintuitive property of Gaussian states: the presence of classical correlations necessarily requires the presence of quantum correlations. Finally, our results also shed new light on a protocol for remote activation of entanglement by a third party.     

Entanglement evolution of three-qubit mixed states in multipartite cavity—reservoir systems

We analyze the multipartite entanglement evolution of three-qubit mixed states composed of a GHZ state and a W state.For a composite system consisting of three cavities interacting with independent reservoirs,it is shown that the entanglement evolution is restricted by a set of monogamy relations.Furthermore,as quantified by the negativity,the entanglement dynamical property of the mixed entangled state of cavity photons is investigated.It is found that the three cavity photons can exhibit the phenomenon of entanglement sudden death(ESD).However,compared with the evolution of a generalized three-qubit GHZ state which has the equal initial entanglement,the ESD time of mixed states is later than that of the pure state.Finally,we discuss the entanglement distribution in the multipartite system,and point out the intrinsic relation between the ESD of cavity photons and the entanglement sudden birth of reservoirs.     

Quadratic bell inequalities as tests for multipartite entanglement

This Letter presents quantum mechanical inequalities which distinguish, for systems of n spin- 1 / 2 particles ( n>2), between fully entangled states and states in which at most n-1 particles are entangled. These inequalities are stronger than those obtained by Gisin and Bechmann-Pasquinucci [Phys. Lett. A 246, 1 (1998)] and by Seevinck and Svetlichny [quant-ph/0201046].     

Strong-driving-assisted multipartite entanglement in cavity QED

We propose a method of generating multipartite entanglement by considering the interaction of a system of N two-level atoms in a cavity of high quality factor with a strong classical driving field. It is shown that, with a judicious choice of the cavity detuning and the applied coherent field detuning, vacuum Rabi coupling produces a large number of important multipartite entangled states. It is even possible to produce entangled states involving different cavity modes. Tuning of parameters also permits us to switch from Jaynes-Cummings to anti-Jaynes-Cummings-like interaction.     

Evolution and symmetry of multipartite entanglement

We discover a simple factorization law describing how multipartite entanglement of a composite quantum system evolves when one of the subsystems undergoes an arbitrary physical process. This multipartite entanglement decay is determined uniquely by a single factor we call the entanglement resilience factor. Since the entanglement resilience factor is a function of the quantum channel alone, we find that multipartite entanglement evolves in exactly the same way as bipartite (two qudits) entanglement. For the two qubits case, our factorization law reduces to the main result of [T. Konrad, Nature Phys. 4, 99 (2008)10.1038/nphys885]. In addition, for a permutation P, we provide an operational definition of P asymmetry of entanglement, and find the conditions when a permuted version of a state can be achieved by local means.     

Separable multipartite mixed states: operational asymptotically necessary and sufficient conditions

We introduce an operational procedure to determine, with arbitrary probability and accuracy, optimal entanglement witnesses for every multipartite entangled state. This method provides an operational criterion for separability which is asymptotically necessary and sufficient. Our results are also generalized to detect all different types of multipartite entanglement.     

Optimized monogamy and polygamy inequalities for multipartite qubit entanglement

We investigate the monogamy and polygamy inequalities of arbitrary multipartite quantum states, and provide new classes of monogamy and polygamy inequalities of multiqubit entanglement in terms of concurrence, entanglement of formation, negativity, and Tsallis-q entanglement, respectively. We show that these new monogamy and polygamy inequality relations are tighter than the existing ones with detailed examples.     

Robustness of multipartite entanglement under collisional decoherence

The collision model of Ziman et al. was considered and the robustness of N-qubit Greenberger-Horne-Zeilinger (GHZ), W, and linear cluster states were studied. Our results show that N-qubit entanglement of GHZ states would be extremely fragile under collisional decoherence, and that of W states could be more robust than of linear cluster states. The text was submitted by the author in English.     

Detection of multipartite entanglement with two-body correlations

We show how to detect entanglement with criteria built from simple two-body correlation terms. Since many natural Hamiltonians are sums of such correlation terms, our ideas can be used to detect entanglement by energy measurement. Our criteria can straightforwardly be applied for detecting different forms of multipartite entanglement in familiar spin models in thermal equilibrium. PACS 03.65.Ud; 03.67.Mn; 05.50.+q