In every dimension d≥3, every admissible fixed-cost quantum coupling violates the triangle inequality, so no fixed cost operator yields a quantum Wasserstein metric on all states.
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No-Go Theorems for Quantum Transport Metrics from Fixed Cost Operators
In every dimension d≥3, every admissible fixed-cost quantum coupling violates the triangle inequality, so no fixed cost operator yields a quantum Wasserstein metric on all states.