Optimality of generalized Choi maps in $M_3$

• URL: http://arxiv.org/abs/2312.02814v1
• Date: Tue, 5 Dec 2023 14:57:11 GMT
• Title: Optimality of generalized Choi maps in $M_3$
• Authors: Giovanni Scala, Anindita Bera, Gniewomir Sarbicki, Dariusz Chru\'sci\'nski
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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