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From unextendible product bases to genuinely entangled subspaces

Abstract

Unextendible product bases (UPBs) are interesting mathematical objects arising in composite Hilbert spaces that have found various applications in quantum information theory, for instance in a construction of bound entangled states or Bell inequalities without quantum violation. They are closely related to another important notion, completely entangled subspaces (CESs), which are those that do not contain any fully separable pure state. Among CESs one finds a class of subspaces in which all vectors are not only entangled but genuinely entangled. Here we explore the connection between UPBs and such genuinely entangled subspaces (GESs) and provide classes of nonorthogonal UPBs that lead to GESs for any number of parties and local dimensions. We then show how these subspaces can be immediately utilized for a simple general construction of genuinely entangled states in any such multipartite scenario.

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Category:
Articles
Type:
artykuł w czasopiśmie wyróżnionym w JCR
Published in:
PHYSICAL REVIEW A no. 98, edition 1, pages 1 - 13,
ISSN: 2469-9926
Language:
English
Publication year:
2018
Bibliographic description:
Demianowicz M., Augusiak R.: From unextendible product bases to genuinely entangled subspaces// PHYSICAL REVIEW A. -Vol. 98, iss. 1 (2018), s.1-13
DOI:
Digital Object Identifier (open in new tab) 10.1103/physreva.98.012313
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