Entangled states with positive partial transpose arising from indecomposable positive linear maps

Abstract

We construct entangled states with positive partial transposes using indecomposable positive linear maps between matrix algebras. We also exhibit concrete examples of entangled states with positive partial transposes arising in this way, and show that they generate extreme rays in the cone of all positive semi-definite matrices with positive partial transposes. They also have Schmidt numbers two.

16 pages

References in corpus (7)

• Separability of Mixed States: Necessary and Sufficient Conditions
• Separability criterion and inseparable mixed states with positive partial transposition
• Unextendible Product Bases and Bound Entanglement
• A Schmidt number for density matrices
• Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
• Schmidt number witnesses and bound entanglement
• Product Bases in Quantum Information Theory

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