Rank Two Bipartite Bound Entangled States Do Not Exist
| dc.creator | Horodecki, Pawel | |
| dc.creator | Smolin, John A. | |
| dc.creator | Terhal, Barbara M. | |
| dc.creator | Thapliyal, Ashish V. | |
| dc.date | 1999-10-29 | |
| dc.date | 2001-08-16 | |
| dc.date.accessioned | 2026-07-07T06:17:08Z | |
| dc.date.available | 2026-07-07T06:17:08Z | |
| dc.description | 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 \times 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. | |
| dc.description | 5 pages LaTeX, many corrections and updated references | |
| dc.identifier | https://arxiv.org/abs/quant-ph/9910122 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/9910122 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/94296 | |
| dc.subject | Quantum Physics | |
| dc.title | Rank Two Bipartite Bound Entangled States Do Not Exist | |
| dc.type | text |