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

• URL: http://arxiv.org/abs/2011.03809v2
• Date: Fri, 15 Apr 2022 18:15:04 GMT
• Title: The PPT$^2$ conjecture holds for all Choi-type maps
• Authors: Satvik Singh and Ion Nechita
• Abstract summary: 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. 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.
• Score: 1.5229257192293197
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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