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arXiv · 2607.07764

Comment on 'Quantum Monge-Kantorovich Problem and Transport Distance between Density Matrices'

Tomasz Miller
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Abstract

Friedland et al. [PRL 129, 110402 (2022)] proposed and studied a quantum analogue of the $p$-Wasserstein distance based on quantum cost matrices and quantum couplings. They conjectured that, despite being only a semidistance in general, this quantity is a true distance for a particular quantum cost matrix and for cost matrices in a small neighborhood of it. We disprove these conjectures by exhibiting an explicit family of triples of states for which the triangle inequality fails.

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Tomasz Miller. 2026-07-08. Comment on 'Quantum Monge-Kantorovich Problem and Transport Distance between Density Matrices'. https://arxiv.org/abs/2607.07764

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