The PPT$^2$ conjecture holds for all Choi-type maps

TL;DR

This paper proves the PPT$^2$ conjecture for a class of covariant linear maps, including many important quantum channels, using a generalized matrix factorization approach.

Contribution

It establishes the conjecture for Choi-type and related maps by extending the concept of factor width for pairwise completely positive matrices.

Findings

PPT$^2$ conjecture holds for covariant maps under diagonal unitary group

Complete characterization of factor width two for pairwise completely positive matrices

Application to Choi-type, depolarizing, dephasing, and amplitude damping maps

Abstract

We prove that the PPT$^2$ conjecture holds for linear maps between matrix algebras which are covariant under the action of the diagonal unitary group. Many salient examples, like the Choi-type maps, depolarizing maps, dephasing maps, amplitude damping maps, and mixtures thereof, lie in this class. Our proof relies on a generalization of the matrix-theoretic notion of factor width for pairwise completely positive matrices, and a complete characterization in the case of factor width two.