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On the monotonicity of a quantum optimal transport cost

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arxiv 2211.11713 v1 pith:DEDCZWVH submitted 2022-11-21 quant-ph math-phmath.MP

Alexander Müller-Hermes This is my paper · ORCID
classification quant-phmath-phmath.MP
keywords quantummonotoneunderapplicationchakrabartichannelsconjecturecost
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abstract

We show that the quantum generalization of the $2$-Wasserstein distance proposed by Chakrabarti et al. is not monotone under partial traces. This disproves a recent conjecture by Friedland et al. Finally, we propose a stabilized version of the original definition, which we show to be monotone under the application of general quantum channels.

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  1. Complete Quantum Relational Hoare Logics from Optimal Transport Duality

    cs.LO 2025-01 accept novelty 8.0 of 10

    A sound and complete quantum relational Hoare logic (qOTL) for almost-surely terminating programs with bounded postconditions is obtained by adding a duality rule based on quantum optimal transport.

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