Wasserstein distances and divergences of order p by quantum channels

2025/01/14 by Gergely Bunth, Bunth, Gergely, József Pitrik +5 · 6 citations
Mathematics · #81P16. Secondary: 81Q10 #Advanced Mathematical Identities #FOS: Mathematics #FOS: Physical sciences #Graph theory and applications #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Primary: 49Q22 #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2501.08066

openalex publication_date 2025/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a non-quadratic generalization of the quantum mechanical optimal transport problem introduced in [De Palma and Trevisan, Ann. Henri Poincaré, \bf 22 (2021), 3199-3234] where quantum channels realize the transport. Relying on this general machinery, we introduce p-Wasserstein distances and divergences and study their fundamental geometric properties. Finally, we prove triangle inequality for quadratic Wasserstein divergences under the sole assumption that an arbitrary one of the states involved is pure, which is a generalization of our previous result in this direction.

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