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

• URL: http://arxiv.org/abs/2609.03769v1
• Date: Thu, 03 Sep 2026 12:36:28 GMT
• Title: Metricity of separable quantum optimal transport with the Hilbert-Schmidt cost
• Abstract summary: We prove that the square root of the separable quantum optimal transport cost associated with the projection onto the antisymmetric subspace defines a genuine distance between density matrices.<n>This establishes the triangle inequality for the order-two Beatty-Frana quantum optimal transport construction induced by the Hilbert-Schmidt distance between pure states.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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