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arXiv · 2605.03027

Relations between different definitions of the quantum Wasserstein distance

Géza Tóth·József Pitrik
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Abstract

The quantum Wasserstein distances defined by Golse, Mouhot, Paul, and Caglioti and by De Palma and Trevisan coincide for qubits when a single operator appears in the cost function. As a consequence, the square of the self-distance equals the Wigner-Yanase skew information in this case. Moreover, for finite-dimensional systems of dimension $d\ge2$ and any number of operators, we show that the Golse-Mouhot-Paul-Caglioti self-distance is bounded from below by the De Palma-Trevisan self-distance.

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Géza Tóth, József Pitrik. 2026-09-16. Relations between different definitions of the quantum Wasserstein distance. https://arxiv.org/abs/2605.03027

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