Unextendible Product Bases and Bound Entanglement

Details Unextendible Product Bases and Bound Entanglement Unextendible Product Bases and Bound Entanglement

1998-08-18

arxiv.org/abs/quant-ph/9808030v2

Phys.Rev.Lett. 82 (1999) 5385

Physics

Quantum Physics

4 pages RevTex + 1 eps fig. This is version 2 with many changes and simplifications, and an additional author

Scientific paper

10.1103/PhysRevLett.82.5385

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 2x2x2 UPB whose complementary mixed state has tripartite entanglement but no bipartite entanglement, i.e. all three corresponding 2x4 bipartite mixed states are unentangled. We show that members of a UPB are not perfectly distinguishable by local POVMs and classical communication.

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