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Quantum Information Processing

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01-06-2016

Separability conditions based on local fine-grained uncertainty relations

Author: Alexey E. Rastegin

Published in: Quantum Information Processing | Issue 6/2016

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Abstract

Many protocols of quantum information processing use entangled states. Hence, separability criteria are of great importance. We propose new separability conditions for a bipartite finite-dimensional system. They are derived by using fine-grained uncertainty relations. Fine-grained uncertainty relations can be obtained by consideration of the spectral norms of certain positive matrices. One of possible approaches to separability conditions is connected with upper bounds on the sum of maximal probabilities. Separability conditions are often formulated for measurements that have a special structure. For instance, mutually unbiased bases and mutually unbiased measurements can be utilized for such purposes. Using resolution of the identity for each subsystem of a bipartite system, we construct some resolution of the identity in the product of Hilbert spaces. Separability conditions are then formulated in terms of maximal probabilities for a collection of specific outcomes. The presented conditions are compared with some previous formulations. Our results are exemplified with entangled states of a two-qutrit system.

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Title: Separability conditions based on local fine-grained uncertainty relations
Author: Alexey E. Rastegin
Publication date: 01-06-2016
Publisher: Springer US
Published in: Quantum Information Processing / Issue 6/2016
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI: https://doi.org/10.1007/s11128-016-1286-z

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