Algebraic, Operational and Denotational Semantics for Classically Controlled Quantum Communication
PLanQC 2025, 2025, with Sam Staton.
[Paper Abstract] We systematically study the semantics of classically controlled quantum communication. We present a parameterised algebraic theory for classically controlled quantum I/O, and give two sound models: a quantum-stream-based operational semantics, and a monadic denotational semantics. We further show that the two models correspond to the same notion of communication in the sense that the latter is adequate and fully abstract with respect to the former.