Li JL, Qiao CF. A Necessary and Sufficient Criterion for the Separability of Quantum State.
Sci Rep 2018;
8:1442. [PMID:
29362415 PMCID:
PMC5780502 DOI:
10.1038/s41598-018-19709-z]
[Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2017] [Accepted: 01/05/2018] [Indexed: 11/29/2022] Open
Abstract
Quantum entanglement has been regarded as one of the key physical resources in quantum information sciences. However, the determination of whether a mixed state is entangled or not is generally a hard issue, even for the bipartite system. In this work we propose an operational necessary and sufficient criterion for the separability of an arbitrary bipartite mixed state, by virtue of the multiplicative Horn’s problem. The work follows the work initiated by Horodecki et al. and uses the Bloch vector representation introduced to the separability problem by J. De Vicente. In our criterion, a complete and finite set of inequalities to determine the separability of compound system is obtained, which may be viewed as trade-off relations between the quantumness of subsystems. We apply the obtained result to explicit examples, e.g. the separable decomposition of arbitrary dimension Werner state and isotropic state.
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