Unextendible Product Bases and Locally Unconvertible Bound Entangled States |
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Authors: | Email author" target="_blank">S?B?BravyiEmail author |
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Affiliation: | (1) Institute for Quantum Information, California Institute of Technology, Pasadena, 91125, CA, USA |
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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 S and 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 (S,T) > 0 such that for any LOCC protocol mapping S into a probabilistic ensemble (p, ), the fidelity between T and any possible final state satisfies F(T, ) = 1 - (S,T).PACS: 03.65.Bz; 03.67.-a; 89.70+c. |
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Keywords: | unextendible product bases bound entanglement LOCC |
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