Choi matrices, norms and entanglement associated with positive maps on matrix algebras

TL;DR

This paper investigates positive maps between matrix algebras, focusing on Choi matrices, their norms, and entanglement properties, with implications for quantum state distillability and k-positivity.

Contribution

It provides new insights into how Choi matrices and their norms relate to properties like entanglement and k-positivity, including partial results on quantum state distillability.

Findings

Choi matrices reflect properties of positive maps.

Norm estimates relate to entanglement and k-positivity.

Partial results on n-copy distillability of quantum states.

Abstract

We study positive maps of B(K) into B(H) for finite-dimensional Hilbert spaces K and H. Our main emphasis is on how Choi matrices and estimates of their norms with respect to mapping cones reflect various properties of the maps. Special attention will be given to entanglement properties and k-positive maps, in particular tensor products of 2-positive maps. The latter problem is directly related to the question of n-copy distillability of quantum states, for which we obtain a partial result.