AD-HMC achieves geometric convergence in Wasserstein distance for HMC with general asymmetrical auxiliary momentum distributions by restoring self-adjointness via direction alternation, with extensions to leapfrog integrators.
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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.
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Hamiltonian Monte Carlo with Asymmetrical Momentum Distributions
AD-HMC achieves geometric convergence in Wasserstein distance for HMC with general asymmetrical auxiliary momentum distributions by restoring self-adjointness via direction alternation, with extensions to leapfrog integrators.
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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.