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arXiv · 2609.03769

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

Tomasz Miller
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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-Fran\c{c}a 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.

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Tomasz Miller. 2026-09-03. Metricity of separable quantum optimal transport with the Hilbert-Schmidt cost. https://arxiv.org/abs/2609.03769

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