Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement

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dc.creatorDiVincenzo, David P.
dc.creatorMor, Tal
dc.creatorShor, Peter W.
dc.creatorSmolin, John A.
dc.creatorTerhal, Barbara M.
dc.date1999-08-22
dc.date2000-11-06
dc.date.accessioned2026-07-07T06:16:53Z
dc.date.available2026-07-07T06:16:53Z
dc.descriptionWe report new results and generalizations of our work on unextendible product bases (UPB), uncompletable product bases and bound entanglement. We present a new construction for bound entangled states based on product bases which are only completable in a locally extended Hilbert space. We introduce a very useful representation of a product basis, an orthogonality graph. Using this representation we give a complete characterization of unextendible product bases for two qutrits. We present several generalizations of UPBs to arbitrary high dimensions and multipartite systems. We present a sufficient condition for sets of orthogonal product states to be distinguishable by separable superoperators. We prove that bound entangled states cannot help increase the distillable entanglement of a state beyond its regularized entanglement of formation assisted by bound entanglement.
dc.description24 pages RevTex, 15 figures; appendix removed, several small corrections, to appear in Comm. Math. Phys
dc.identifierhttps://arxiv.org/abs/quant-ph/9908070
dc.identifierhttp://arxiv.org/abs/quant-ph/9908070
dc.identifierComm. Math. Phys. 238, pp. 379--410 (2003)
dc.identifierdoi:10.1007/s00220-003-0877-6
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/94217
dc.subjectQuantum Physics
dc.titleUnextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
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