An explicit three-parameter family of diagonal states disproves the conjectures that the quantum 2-Wasserstein quantity for the antisymmetric cost matrix (and nearby matrices) is a true distance.
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Comment on 'Quantum Monge-Kantorovich Problem and Transport Distance between Density Matrices'
An explicit three-parameter family of diagonal states disproves the conjectures that the quantum 2-Wasserstein quantity for the antisymmetric cost matrix (and nearby matrices) is a true distance.