Open AccessUnextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
Author(s) -
David P. DiVincenzo,
Tal Mor,
Peter W. Shor,
John A. Smolin,
Barbara M. Terhal
Publication year - 2003
Publication title -
communications in mathematical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.662
H-Index - 152
eISSN - 1432-0916
pISSN - 0010-3616
DOI - 10.1007/s00220-003-0877-6
Subject(s) - quantum entanglement , multipartite , product (mathematics) , basis (linear algebra) , hilbert space , multipartite entanglement , mathematics , orthogonality , separable space , representation (politics) , upper and lower bounds , combinatorics , separable state , squashed entanglement , discrete mathematics , pure mathematics , quantum mechanics , physics , quantum , mathematical analysis , geometry , quantum discord , politics , political science , law
We report new results and generalizations of our work on unextendible productbases (UPB), uncompletable product bases and bound entanglement. We present anew construction for bound entangled states based on product bases which areonly completable in a locally extended Hilbert space. We introduce a veryuseful representation of a product basis, an orthogonality graph. Using thisrepresentation we give a complete characterization of unextendible productbases for two qutrits. We present several generalizations of UPBs to arbitraryhigh dimensions and multipartite systems. We present a sufficient condition forsets of orthogonal product states to be distinguishable by separablesuperoperators. We prove that bound entangled states cannot help increase thedistillable entanglement of a state beyond its regularized entanglement offormation assisted by bound entanglement.Comment: 24 pages RevTex, 15 figures; appendix removed, several small corrections, to appear in Comm. Math. Phy
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