Separable decompositions of bipartite mixed states

Li, Jun-Li

doi:10.1007/s11128-018-1862-5

Cited by 8 publications

(8 citation statements)

References 24 publications

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“…Also, our method leads to a practical entanglement criterion for bipartite mixed states. Considering the important roles it plays in the separability problem [32,37], we believe the Bloch representation can be as a useful tool for further quantitative study and deeper understanding of the fundamental concepts in quantum theory, e.g. the uncertainty relation, quantum entanglement, and quantum steering [38].…”

Section: Discussionmentioning

confidence: 99%

State-independent uncertainty relations and entanglement detection

Chen

2018

Quantum Inf Process

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The uncertainty relation is one of the key ingredients of quantum theory. Despite the great efforts devoted to this subject, most of the variance-based uncertainty relations are state-dependent and suffering from the triviality problem of zero lower bounds. Here we develop a method to get uncertainty relations with state-independent lower bounds. The method works by exploring the eigenvalues of a Hermitian matrix composed by Bloch vectors of incompatible observables and is applicable for both pure and mixed states and for arbitrary number of Ndimensional observables. The uncertainty relation for incompatible observables can be explained by geometric relations related to the parallel postulate and the inequalities in Horn's conjecture on Hermitian matrix sum. Practical entanglement criteria are also presented based on the derived uncertainty relations.

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Section: Discussionmentioning

confidence: 99%

State-independent uncertainty relations and entanglement detection

Chen

2018

Quantum Inf Process

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“…According to the Corollary 1 of Ref. [18], for our aim, we only need to consider the state with full local rank, say,…”

Section: General Representation Of the Biparitite Separable Statementioning

confidence: 99%

The Decompositions of Werner and Isotropic States

Yang,

Li,

Qiao

2020

Preprint

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The well-known tough issue of the decomposition of separable Werner and Isotropic states is investigated in the Bloch representation. Thanks to the existence of SIC-POVM in arbitrary dimentional Hilbert space, we successively obtain the decomposition forms for any separable Werner states. And, by means of the relation between Werner state and Isotropic state, we can get as well the decomposition forms for separable Isotropic states. A geometrical interpretation of the decomposition feasibility in our scheme is given.

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“…We further note that the two-quaterbit counterpart to the two-qubit and two-rebit induced measure formulas (A1) and (22), is [ [40,41].…”

Section: Quaternionic Formulasmentioning

confidence: 99%