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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General criteria extend L^p-mean Wasserstein convergence rates of occupation measures to non-stationary or non-Markovian ergodic processes under conditional convergence to equilibrium, with applications to Brownian diffusions and fractional Brownian driven SDEs.
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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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Convergence rate of the occupation measure of classes of ergodic processes toward their invariant distribution in mean Wasserstein distance
General criteria extend L^p-mean Wasserstein convergence rates of occupation measures to non-stationary or non-Markovian ergodic processes under conditional convergence to equilibrium, with applications to Brownian diffusions and fractional Brownian driven SDEs.