Separability in terms of a single entanglement witness

Piotr Badziąg; Paweł Horodecki; Ryszard Horodecki; Remigiusz Augusiak

Separability in terms of a single entanglement witness

Abstract

The separability problem is formulated in terms of a characterization of a single entanglement witness. More specifically, we show that any (in general multipartite) state rho is separable if and only if a specially constructed entanglement witness W-rho is weakly optimal, i.e., its expectation value vanishes on at least one product vector. Interestingly, the witness can always be chosen to be decomposable. Our result changes the conceptual aspect of the separability problem and raises some questions about the properties of positive maps.

Authors (4)

Piotr Badziąg
- University of Stockholm Alba Nova Fysikum
Paweł Horodecki prof. dr hab.
Ryszard Horodecki
- University of Gdańsk Institute of Theoretical Physics and Astrophysics
Remigiusz Augusiak

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Publication version: Accepted or Published Version
License: Copyright (2013 American Physical Society)

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Category:: Articles
Type:: artykuł w czasopiśmie wyróżnionym w JCR
Published in:: PHYSICAL REVIEW A no. 88, edition 1, pages 1 - 5,
ISSN: 2469-9926
Language:: English
Publication year:: 2013
Bibliographic description:: Badziąg P., Horodecki P., Horodecki R., Augusiak R.: Separability in terms of a single entanglement witness// PHYSICAL REVIEW A. -Vol. 88, iss. 1 (2013), s.1-5
Verified by:: Gdańsk University of Technology