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arXiv:2304.00309 · Linear Algebra and its Applications

Degradable strong entanglement breaking maps

Repana Devendra, Gunjan Sapra, K. Sumesh

Published Sep 17, 2024• 1 citation
arXivHTMLPDF
DOI
10.1016/j.laa.2024.09.006

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An s-entanglement breaking map between operator systems is a point-norm limit of entanglement breaking maps, which are a generalization of the corresponding notion in matrix algebras. We develop some of the key properties of this map, and obtain some conditions when the completely positive linear maps between operator systems coincide with the s-entanglement breaking maps. Especially we show that a linear map from a nuclear operator system to the maximal operator system structure of an Archimedean ordered * -vector space is completely positive if and only if it is s-entanglement breaking. We also discuss the relationships between s-entanglement breaking maps and weak * -entanglement breaking maps, and nuclear maps between operator systems.
We prove that every PPT linear map has finite entanglement breaking index, thereby establishing the eventual entanglement breaking property of PPT channels in full generality. Furthermore, by utilizing completely positive maps with low entanglement dimensionality, we show that a large family of PPT maps, which strictly contains the class of 2-superpositive maps, has entanglement breaking index bounded above by 3, uniformly in the dimension. In particular, these results provide evidence that the PPT-cubed conjecture may hold in full generality.