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arXiv · 2312.02814

Optimality of generalized Choi maps in $M_3$

Giovanni Scala·Anindita Bera·Gniewomir Sarbicki·Dariusz Chruściński
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Abstract

A family of linear positive maps in the algebra of $3 \times 3$ complex matrices proposed recently in Bera et al. arXiv:2212.03807 is further analyzed. It provides a generalization of a seminal Choi nondecomposable extremal map in $M_3$. We investigate when generalized Choi maps are optimal, i.e. cannot be represented as a sum of positive and completely positive maps. This property is weaker than extremality, however, it turns out that it plays a key role in detecting quantum entanglement.

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Giovanni Scala, Anindita Bera, Gniewomir Sarbicki, Dariusz Chruściński. 2023-12-05. Optimality of generalized Choi maps in $M_3$. https://arxiv.org/abs/2312.02814

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