Defines Ollivier-Ricci curvature for causal sets using Lorentzian optimal transport, proves local-to-global and Bonnet-Myers results, and validates numerically on sprinkled constant-curvature spacetimes.
von Renesse and Karl-Theodor Sturm
4 Pith papers cite this work. Polarity classification is still indexing.
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Establishes Kantorovich duality for linearized non-quadratic quantum optimal transport realized by channels, determines optimal primal-dual solutions for qubits under state restrictions, and proves the triangle inequality for the square of the induced quantum Wasserstein divergences.
Defines p-Wasserstein distances and divergences via quantum channels and proves triangle inequality for quadratic divergences assuming one state is pure.
A literature review synthesizing developments in quantum Wasserstein distances, their applications, and unresolved questions.
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Ollivier-Ricci Curvature for Causal Sets
Defines Ollivier-Ricci curvature for causal sets using Lorentzian optimal transport, proves local-to-global and Bonnet-Myers results, and validates numerically on sprinkled constant-curvature spacetimes.
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Strong Kantorovich duality for quantum optimal transport with generic cost and optimal couplings on quantum bits
Establishes Kantorovich duality for linearized non-quadratic quantum optimal transport realized by channels, determines optimal primal-dual solutions for qubits under state restrictions, and proves the triangle inequality for the square of the induced quantum Wasserstein divergences.
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Wasserstein distances and divergences of order $p$ by quantum channels
Defines p-Wasserstein distances and divergences via quantum channels and proves triangle inequality for quadratic divergences assuming one state is pure.
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Wasserstein Distances on Quantum Structures: an Overview
A literature review synthesizing developments in quantum Wasserstein distances, their applications, and unresolved questions.