Develops and proves a Pontryagin-type maximum principle for control problems in free probability using controlled forward equations and free backward SDEs.
Tracial smooth functions of non-commuting variables and the free Wasserstein manifold.Dissertationes Math.
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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.
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Pontryagin Maximum Principle in Free Probability Theory
Develops and proves a Pontryagin-type maximum principle for control problems in free probability using controlled forward equations and free backward 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.