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).
Quantum Information Processing – Springer Journals
Published: Aug 3, 2004
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