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We propose a new generalization to quantum states of the Wasserstein distance, which is a fundamental distance between probability distributions given by the minimization of a transport cost.
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Elements of Information Theory
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A mass transportation approach to quantitative isoperimetric inequalities
A. Figalli, F. Maggi, and A. Pratelli · 2010
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Matrix optimal mass transport: A quantum mechanical approach
Yongxin Chen, Tryphon T. Georgiou, and Allen R. Tannenbaum · 2018
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Yongxin Chen, Tryphon T Georgiou, and Allen Tannenbaum · 2018
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The conditional Entropy Power Inequality for quantum additive noise channels
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Towards optimal transport for quantum densities
Emanuele Caglioti, François Golse, and Thierry Paul · 2018
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The quantum N-body problem in the mean-field and semiclassical regime
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Scaling hypothesis for the euclidean bipartite matching problem
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