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On the monotonicity of a quantum optimal transport cost (2211.11713v1)
Published 21 Nov 2022 in quant-ph, math-ph, and math.MP
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.