A method is given to compute the minimum energy of certain spin Hamiltonians over separable states, expressed via quantum Fisher information for Ising models and fidelity for Heisenberg chains.
Tóth and J
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abstract
We consider several definitions of the quantum Wasserstein distance based on an optimization over general bipartite quantum states with given marginals. Then, we examine the quantities obtained after the optimization is carried out over bipartite separable states instead. We prove that several of these quantities are equal to each other. Thus, we connect several approaches in the literature. We prove the triangle inequality for some of these quantities for the case of one of the three states being pure. As a byproduct, we show that the square root of the Uhlmann-Jozsa quantum fidelity can also be written as an optimization over separable states with given marginals. We use this to prove that some of these quantities equal the Uhlmann-Jozsa quantum fidelity for qubits. We also find relations with the superfidelity.
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UNVERDICTED 2representative citing papers
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.
citing papers explorer
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General method for obtaining the energy minimum of spin Hamiltonians for separable states
A method is given to compute the minimum energy of certain spin Hamiltonians over separable states, expressed via quantum Fisher information for Ising models and fidelity for Heisenberg chains.
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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.