PreprintCC BY 4.0arXiv
Relations between different definitions of the quantum Wasserstein distance
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≥2 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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BibTeX
@misc{toth2026relations,
title = {{Relations between different definitions of the quantum Wasserstein distance}},
author = {Géza Tóth and József Pitrik},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.03027},
eprint = {2605.03027},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.03027},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Relations between different definitions of the quantum Wasserstein distance
AU - Géza Tóth
AU - József Pitrik
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2605.03027
UR - https://arxiv.org/abs/2605.03027
AB - 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≥2 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.
ER -