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.

References in corpus (4)

• Diagonal unitary and orthogonal symmetries in quantum theory
• A graphical calculus for integration over random diagonal unitary matrices
• Can entanglement hide behind triangle-free graphs?
• Investigation of the PPT Squared Conjecture for High Dimensions

Cited by in corpus (13)

• Diagonal unitary and orthogonal symmetries in quantum theory
• 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?
• Symmetric quantum states: a review of recent progress
• A class of optimal positive maps in $M_n$
• Random covariant quantum channels
• The Factor Width Rank of a Matrix
• Eventually entanglement breaking divisible quantum dynamics
• $k$-Positive Maps: New Characterizations and a Generation Method
• A Multiplicative Ergodic Theorem for Bistochastic Ergodic Quantum Processes with Applications to Entanglement
• Rank-based entanglement detection for bound entangled states