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.
The Monge metric onthe sphere and geometry of quantum states
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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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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.