The PPT${}^2$ conjecture holds for all Choi-type 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.

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Cited by in corpus (13)

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• Detecting positive quantum capacities of quantum channels
• Covariance Decomposition as a Universal Limit on Correlations in Networks
• A graphical calculus for integration over random diagonal unitary matrices
• Can entanglement hide behind triangle-free graphs?
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• A Multiplicative Ergodic Theorem for Bistochastic Ergodic Quantum Processes with Applications to Entanglement
• Rank-based entanglement detection for bound entangled states