Phys. Rev. Lett. 82, 5385–5388 (1999)Unextendible Product Bases and Bound EntanglementReceived 20 August 1998; revised 16 February 1999; published in the issue dated 28 June 1999 An unextendible product basis (UPB) for a multipartite quantum system is an incomplete orthogonal product basis whose complementary subspace contains no product state. We give examples of UPBs, and show that the uniform mixed state over the subspace complementary to any UPB is a bound entangled state. We exhibit a tripartite 2×2×2 UPB whose complementary mixed state has tripartite entanglement but no bipartite entanglement, i.e., all three corresponding 2×4 bipartite mixed states are unentangled. We show that members of a UPB are not perfectly distinguishable by local positive operator valued measurements and classical communication. © 1999 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.82.5385
DOI:
10.1103/PhysRevLett.82.5385
PACS:
03.67.Hk, 03.65.Bz, 89.70.+c
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