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arXiv · 2202.00341

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

B. V. Rajarama Bhat·Repana Devendra·Nirupama Mallick·K. Sumesh
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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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BibTeXRIS

B. V. Rajarama Bhat, Repana Devendra, Nirupama Mallick, K. Sumesh. 2022-02-01. $C^*$-extreme points of entanglement breaking maps. https://doi.org/10.1142/s0129055x23500058

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