Unextendible Product Bases and Locally Unconvertible Bound Entangled States

Unextendible Product Bases and Locally Unconvertible Bound Entangled States Mutual convertibility of bound entangled states under local quantum operations and classical communication (LOCC) is studied. We focus on states associated with unextendible product bases (UPB) in a system of three qubits. A complete classification of such UPBs is suggested. We prove that for any pair of UPBs S and T the associated bound entangled states ρ S and ρ T cannot be converted to each other by LOCC, unless S and T coincide up to local unitaries. More specifically, there exists a finite precision ε (S,T) > 0 such that for any LOCC protocol mapping ρ S into a probabilistic ensemble (p α, ρα), the fidelity between ρ T and any possible final state ρα satisfies F(ρ T , ρα) = 1 - ε(S,T). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Unextendible Product Bases and Locally Unconvertible Bound Entangled States

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Publisher
Kluwer Academic Publishers-Plenum Publishers
Copyright
Copyright © 2004 by Springer Science+Business Media, Inc.
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/s11128-004-7076-z
Publisher site
See Article on Publisher Site

Abstract

Mutual convertibility of bound entangled states under local quantum operations and classical communication (LOCC) is studied. We focus on states associated with unextendible product bases (UPB) in a system of three qubits. A complete classification of such UPBs is suggested. We prove that for any pair of UPBs S and T the associated bound entangled states ρ S and ρ T cannot be converted to each other by LOCC, unless S and T coincide up to local unitaries. More specifically, there exists a finite precision ε (S,T) > 0 such that for any LOCC protocol mapping ρ S into a probabilistic ensemble (p α, ρα), the fidelity between ρ T and any possible final state ρα satisfies F(ρ T , ρα) = 1 - ε(S,T).

Journal

Quantum Information ProcessingSpringer Journals

Published: Aug 3, 2004

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