Constructing new optimal entanglement witnesses

Abstract

We provide a new class of indecomposable entanglement witnesses. In 4 x 4 case it reproduces the well know Breuer-Hall witness. We prove that these new witnesses are optimal and atomic, i.e. they are able to detect the "weakest" quantum entanglement encoded into states with positive partial transposition (PPT). Equivalently, we provide a new construction of indecomposable atomic maps in the algebra of 2k x 2k complex matrices. It is shown that their structural physical approximations give rise to entanglement breaking channels. This result supports recent conjecture by Korbicz et. al.

9 pages

References in corpus (12)

• Detecting Genuine Multipartite Entanglement with Two Local Measurements
• Quantifying Entanglement with Witness Operators
• Optimal entanglement criterion for mixed quantum states
• Structural approximations to positive maps and entanglement breaking channels
• Separable Multipartite Mixed States - Operational Asymptotically Necessary and Sufficient Conditions
• Spectral conditions for positive maps
• On circulant states with positive partial transpose
• A new class of states with positive partial transposition
• Spectral properties of entanglement witnesses
• Spectral conditions for entanglement witnesses vs. bound entanglement
• A class of positive atomic maps
• Generalized Circulant Densities and a Sufficient Condition for Separability

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