Unextendible product bases and locally unconvertible bound entangled states

Details Unextendible product bases and locally unconvertible bound entangled states Unextendible product bases and locally unconvertible bound entangled states

2003-10-29

arxiv.org/abs/quant-ph/0310172v1

Quantum Information Processing, Vol. 3(6) pp. 309-329 (2004)

Physics

Quantum Physics

REVTeX, 9 pages, 2 figures

Scientific paper

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 $\rho_S$ and $\rho_T$ can not be converted to each other by LOCC, unless $S$ and $T$ coincide up to local unitaries. More specifically, there exists a finite precision $\epsilon>0$ such that for any LOCC protocol mapping $\rho_S$ into a probabilistic ensemble $(p_j,\rho_j)$, the fidelity between $\rho_T$ and any possible final state $\rho_j$ is smaller than $1-\epsilon$.

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