Two quantum Wasserstein distance definitions coincide for qubits with single-operator cost functions, implying the self-distance equals the Wigner-Yanase skew information.
Quantum Optimal Transport and Weak Topologies
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Proves equalities among quantum Wasserstein distances obtained from optimizations over general versus separable bipartite states and shows relations to Uhlmann-Jozsa fidelity and superfidelity, including equality for qubits.
A literature review synthesizing developments in quantum Wasserstein distances, their applications, and unresolved questions.
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Relations between different definitions of the quantum Wasserstein distance for qubits
Two quantum Wasserstein distance definitions coincide for qubits with single-operator cost functions, implying the self-distance equals the Wigner-Yanase skew information.