QUANTUM LOGICS
Logics and calculi individuated by quantum structure: systems whose connectives, states, or processes reflect the non-classical algebra of quantum mechanics—non-distributive lattices of propositions, effect algebras, and the diagrammatic calculi of quantum information. The domain is what unifies them and it is close to the only thing that does: the propositional strand descends from Birkhoff and von Neumann's observation (1936) that the closed subspaces of a Hilbert space fail distribution, since the span of two subspaces contains vectors lying in neither, while the process strand descends from the categorical reconstruction of quantum mechanics in the 2000s, and the two share their subject rather than their machinery.
Entries include the propositional quantum logics (orthologic, effect algebras), the logics of quantum computation and information (quantum computation, information, and programming logic; quantum Hoare logic), the intensional quantum logics (quantum modal and temporal logic), and the process-theoretic and diagrammatic calculi (ZX calculus, quantum process theories).