Abstract
We 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.
Original language | English |
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Pages (from-to) | 379-410 |
Number of pages | 32 |
Journal | Communications in Mathematical Physics |
Volume | 238 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2003 |
Externally published | Yes |
Keywords
- Hilbert Space
- High Dimension
- Entangle State
- Product State
- Complete Characterization