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Separability Criterion for Bipartite States and Its Generalization to Multipartite Systems

。 Huang, Jie-Hui, H. Hu +5 more

Chinese Physics LettersJan 1, 20140 citations

Separability criteria based on the realignment of density matrices and reduced density matrices

Shu‐Qian Shen, Mengyuan Wang, Ming Li +1 more

By combining a parameterized Hermitian matrix, the realignment matrix of the bipartite density matrix, and the vectorization of its reduced density matrices, we present a family of separability criteria which are stronger than the computable cross-norm or realignment (CCNR) criterion. With linear contraction methods, the proposed criteria can be used to detect the multipartite entangled states that are biseparable under any bipartite partitions. Moreover, we show by examples that the presented multipartite separability criteria can be more efficient than the corresponding multipartite realignment criterion based on CCNR, multipartite correlation tensor criterion, and multipartite covariance matrix criterion.By combining a parameterized Hermitian matrix, the realignment matrix of the bipartite density matrix, and the vectorization of its reduced density matrices, we present a family of separability criteria which are stronger than the computable cross-norm or realignment (CCNR) criterion. With linear contraction methods, the proposed criteria can be used to detect the multipartite entangled states that are biseparable under any bipartite partitions. Moreover, we show by examples that the presented multipartite separability criteria can be more efficient than the corresponding multipartite realignment criterion based on CCNR, multipartite correlation tensor criterion, and multipartite covariance matrix criterion.

arXiv:1511.00375Physical Review AOct 29, 201518 citations

Separability criterions of multipartite states

Ying Yang, Huaixin Cao

The European Physical Journal DAug 1, 20184 citations

The distillability of entanglement of bipartite reduced density matrices of a tripartite state

Yize Sun, Lin Chen

Abstract The relation between the distillability of entanglement of three bipartite reduced density matrices from a tripartite pure state has been studied in Hayashi and Chen [2011 Phys. Rev. A 84 012325]. We extend this result to the tripartite mixed state of rank at most three. In particular we show that if the state has two bipartite reduced density operators with rank two, then the third bipartite reduced density operator additionally having non positive partial transpose (non-PPT) is distillable. In contrast, we show that the tripartite PPT state with two reduced density operators of rank two is a three-qubit fully separable state. We obtain these facts by proving a conjectured matrix inequality for the bipartite matrix M with Schmidt rank at most three. This is one of the main results of this paper. We also prove it for some M with arbitrary Schmidt rank.Abstract The relation between the distillability of entanglement of three bipartite reduced density matrices from a tripartite pure state has been studied in Hayashi and Chen [2011 Phys. Rev. A 84 012325]. We extend this result to the tripartite mixed state of rank at most three. In particular we show that if the state has two bipartite reduced density operators with rank two, then the third bipartite reduced density operator additionally having non positive partial transpose (non-PPT) is distillable. In contrast, we show that the tripartite PPT state with two reduced density operators of rank two is a three-qubit fully separable state. We obtain these facts by proving a conjectured matrix inequality for the bipartite matrix M with Schmidt rank at most three. This is one of the main results of this paper. We also prove it for some M with arbitrary Schmidt rank.

Journal of Physics A Mathematical and TheoreticalJun 1, 20204 citations

Criteria for Separability of Multipartite Quantum System

Yuan-Hong Tao, Weiwei Ding, Chang’e Li

International Journal of Theoretical PhysicsNov 7, 20122 citations

AN EFFICIENT SEPARABILITY CRITERION FOR n-PARTITE ARBITRARILY DIMENSIONAL QUANTUM STATES

Yinxiang Long, Daowen Qiu, Dongyang Long

In this paper, we obtain an efficient separability criterion for bipartite quantum pure state systems, which is based on the two-order minors of the coefficient matrix corresponding to quantum state. Then, we generalize this criterion to multipartite arbitrarily dimensional pure states. Our criterion is directly built upon coefficient matrices, but not density matrices or observables, so it has the advantage of being computed easily. Indeed, to judge separability for an arbitrary n-partite pure state in a d-dimensional Hilbert space, it only needs at most O(d) times operations of multiplication and comparison. Our criterion can be extended to mixed states. Compared with Yu's criteria, our methods are faster, and can be applied to any quantum state.In this paper, we obtain an efficient separability criterion for bipartite quantum pure state systems, which is based on the two-order minors of the coefficient matrix corresponding to quantum state. Then, we generalize this criterion to multipartite arbitrarily dimensional pure states. Our criterion is directly built upon coefficient matrices, but not density matrices or observables, so it has the advantage of being computed easily. Indeed, to judge separability for an arbitrary n-partite pure state in a d-dimensional Hilbert space, it only needs at most O(d) times operations of multiplication and comparison. Our criterion can be extended to mixed states. Compared with Yu's criteria, our methods are faster, and can be applied to any quantum state.

International Journal of Quantum InformationJun 1, 20110 citations

Separability Criterion for Arbitrary Multipartite Pure State Based on the Rank of Reduced Density Matrix

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