Complete Relational Logic for Infinite-Dimensional Quantum Programs with Unbounded Assertions
We present sound and complete relational program logics for infinite-dimensional quantum and classical-quantum programs. The logics model assertions as self-adjoint unbounded linear relations, which simultaneously support quantitative and qualitative reasoning. Our main theoretical results include new convergence theorems and infinite-dimensional duality theorems for infinite-dimensional quantum states, which we use to establish completeness.
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