dorsal/arxiv
View SchemaRank Two Bipartite Bound Entangled States Do Not Exist
| Authors | Pawel Horodecki, John A. Smolin, Barbara M. Terhal, Ashish V. Thapliyal |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9910122 |
| URL | https://arxiv.org/abs/quant-ph/9910122 |
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 \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.
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"abstract": "We explore the relation between the rank of a bipartite density matrix and\nthe existence of bound entanglement. We show a relation between the rank,\nmarginal ranks, and distillability of a mixed state and use this to prove that\nany rank n bound entangled state must have support on no more than an n \\times\nn Hilbert space. A direct consequence of this result is that there are no\nbipartite bound entangled states of rank two. We also show that a separability\ncondition in terms of a quantum entropy inequality is associated with the above\nresults. We explore the idea of how many pure states are needed in a mixture to\ncancel the distillable entanglement of a Schmidt rank n pure state and provide\na lower bound of n-1. We also prove that a mixture of a non-zero amount of any\npure entangled state with a pure product state is distillable.",
"arxiv_id": "quant-ph/9910122",
"authors": [
"Pawel Horodecki",
"John A. Smolin",
"Barbara M. Terhal",
"Ashish V. Thapliyal"
],
"categories": [
"quant-ph"
],
"title": "Rank Two Bipartite Bound Entangled States Do Not Exist",
"url": "https://arxiv.org/abs/quant-ph/9910122"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "a1f46012-de7b-44e2-9de8-82c02ce042ed",
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