$C^*$-extreme points of entanglement breaking maps

• URL: http://arxiv.org/abs/2202.00341v1
• Date: Tue, 1 Feb 2022 11:27:09 GMT
• Title: $C^*$-extreme points of entanglement breaking maps
• Authors: B. V. Rajarama Bhat, Repana Devendra, Nirupama Mallick, K. Sumesh
• Abstract summary: We give a complete description of the unital breaking set $C*$-extreme points. Finally, as a direct consequence of the Holevo analogue of EB-maps, we derive a noncommutative form of EB-maps.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper we study the $C^*$-convex set of unital entanglement breaking (EB-)maps on matrix algebras. General properties and an abstract characterization of $C^*$-extreme points are discussed. By establishing a Radon-Nikodym type theorem for a class of EB-maps we give a complete description of the $C^*$-extreme points. It is shown that a unital EB-map $\Phi:M_{d_1}\to M_{d_2}$ is $C^*$-extreme if and only if it has Choi-rank equal to $d_2$. Finally, as a direct consequence of the Holevo form of EB-maps, we derive a noncommutative analogue of the Krein-Milman theorem for $C^*$-convexity of the set of unital EB-maps.

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