On the monotonicity of a quantum optimal transport cost

• URL: http://arxiv.org/abs/2211.11713v1
• Date: Mon, 21 Nov 2022 18:33:50 GMT
• Title: On the monotonicity of a quantum optimal transport cost
• Authors: Alexander M\"uller-Hermes
• Abstract summary: We show that the generalization of the $2$-Wasserstein distance proposed by Chakrabarti et al. is not monotone under partial traces. We propose a stabilized version of the original definition, which we show to be monotone under the application of general quantum channels.
• Score: 91.3755431537592
• License: http://creativecommons.org/licenses/by/4.0/
• 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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