Abstract
We explore the relation between the rank of a bipartite density matrix and the existence of bound entanglement. We show a relation between the rank, marginal ranks, and distillability of a mixed state and use this to prove that any rank n bound entangled state must have support on no more than an n × n Hilbert space. A direct consequence of this result is that there are no bipartite bound entangled states of rank two. We also show that a separability condition in terms of a quantum entropy inequality is associated with the above results. We explore the idea of how many pure states are needed in a mixture to cancel the distillable entanglement of a Schmidt rank n pure state and provide a lower bound of n - 1. We also prove that a mixture of a non-zero amount of any pure entangled state with a pure product state is distillable.
Original language | English |
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Pages (from-to) | 589-596 |
Number of pages | 8 |
Journal | Theoretical Computer Science |
Volume | 292 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2003 |
Externally published | Yes |
Event | Algorithms in Quantum Information Processing - Chicago, IL, United States Duration: 18 Jan 1999 → 22 Jan 1999 |