Metricity of separable quantum optimal transport with the Hilbert-Schmidt cost

Abstract:We prove that the square root of the separable quantum optimal transport cost associated with the orthogonal projection onto the antisymmetric subspace defines a genuine distance between density matrices. Equivalently, this establishes the triangle inequality for the order-two Beatty-França quantum optimal transport construction induced by the Hilbert-Schmidt distance between pure states. The result also proves metricity of the corresponding distance derived from separable SWAP fidelity. The proof replaces the unavailable gluing argument by convex-roof duality and a dimension-independent interpolation result for Hermitian operators.

12 pages, comments are welcome!

arXiv:2609.03769 [quant-ph]

(or arXiv:2609.03769v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.03769 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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