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arXiv · 2501.15238

Complete Quantum Relational Hoare Logics from Optimal Transport Duality

Gilles Barthe·Minbo Gao·Theo Wang·Li Zhou
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Abstract

We introduce a quantitative relational Hoare logic for quantum programs. Assertions of the logic range over a new infinitary extension of positive semidefinite operators. We prove that our logic is sound, and complete for bounded postconditions and almost surely terminating programs. Our completeness result is based on a quantum version of the duality theorem from optimal transport. We also define a complete embedding into our logic of a relational Hoare logic with projective assertions.

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Gilles Barthe, Minbo Gao, Theo Wang, Li Zhou. 2025-01-25. Complete Quantum Relational Hoare Logics from Optimal Transport Duality. https://arxiv.org/abs/2501.15238

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