Completeness for Quantum Relational Hoare Logics
Research Internship Project, 2024, with Gilles Barthe, Minbo Gao, Li Zhou.
[Paper Abstract submitted to LICS 2025] 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.