Mapping cone of $k$-Entanglement Breaking Maps

• URL: http://arxiv.org/abs/2105.14991v2
• Date: Thu, 10 Jun 2021 05:55:42 GMT
• Title: Mapping cone of $k$-Entanglement Breaking Maps
• Authors: Repana Devendra, Nirupama Mallick and K. Sumesh
• Abstract summary: We prove many equivalent conditions for a $k$-positive linear map to be $k$-entanglement breaking. We characterize completely positive maps that reduce Schmidt number on taking composition with another completely positive map.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In \cite{CMW19}, the authors introduced $k$-entanglement breaking linear maps to understand the entanglement breaking property of completely positive maps on taking composition. In this article, we do a systematic study of $k$-entanglement breaking maps. We prove many equivalent conditions for a $k$-positive linear map to be $k$-entanglement breaking, thereby study the mapping cone structure of $k$-entanglement breaking maps. We discuss examples of $k$-entanglement breaking maps and some of their significance. As an application of our study, we characterize completely positive maps that reduce Schmidt number on taking composition with another completely positive map.

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