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The Distance Between Distinctions: Quantum Logical Hamming as a Hilbert--Schmidt Metric

Richard Goodman, Richard Goodman

Published Jul 11, 2026• 0 citations
Publisher

Abstract

The Distance Between Distinctions: Quantum Logical Hamming as a Hilbert--Schmidt Metric
DOI
10.6084/m9.figshare.32964815

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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.