Generalized Wasserstein barycenters on Riemannian manifolds are absolutely continuous when all input measures are absolutely continuous, for strictly convex cost profiles h with singularity at zero, via a geometric approximation approach.
Ricci curvature for metric-measure spaces via optimal transport
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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.
Proves Monge well-posedness and OT-map regularity for linear-quadratic costs (extending Hindawi-Pomet-Rifford 2011 to non-negative costs) and obtains general entropy interpolation inequalities.
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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Absolute continuity of generalized Wasserstein barycenters of finitely many measures
Generalized Wasserstein barycenters on Riemannian manifolds are absolutely continuous when all input measures are absolutely continuous, for strictly convex cost profiles h with singularity at zero, via a geometric approximation approach.
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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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Linear quadratic optimal transport and interpolation inequalities
Proves Monge well-posedness and OT-map regularity for linear-quadratic costs (extending Hindawi-Pomet-Rifford 2011 to non-negative costs) and obtains general entropy interpolation inequalities.
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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.