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arXiv · 2211.11713

On the monotonicity of a quantum optimal transport cost

Alexander Müller-Hermes
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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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Alexander Müller-Hermes. 2022-11-21. On the monotonicity of a quantum optimal transport cost. https://arxiv.org/abs/2211.11713

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