Separability conditions based on local fine-grained uncertainty relations

Separability conditions based on local fine-grained uncertainty relations 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Separability conditions based on local fine-grained uncertainty relations

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Publisher
Springer US
Copyright
Copyright © 2016 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-016-1286-z
Publisher site
See Article on Publisher Site

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