Mapping cone of $k$-Entanglement Breaking Maps

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.

35 pages

References in corpus (4)

• Majorization criterion for distillability of a bipartite quantum state
• Class of PPT bound entangled states associated to almost any set of pure entangled states
• The Jamiołkowski isomorphism and a conceptionally simple proof for the correspondence between vectors having Schmidt number $k$ and $k$-positive maps
• Generation of Mapping Cones from Small Sets

Cited by in corpus (7)

• Annihilating Entanglement Between Cones
• Higher-dimensional entanglement detection and quantum channel characterization using moments of generalized positive maps
• Eventually entanglement breaking divisible quantum dynamics
• Certifying the dimensionality of any quantum channel with minimal assumptions
• Degradable Strongly Entanglement Breaking Maps
• Schoenberg Correspondence for $k$-(Super)Positive Maps on Matrix Algebras
• On the characterization of partially entanglement breaking and annihilating channels