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Compositional and holistic quantum computational semantics. (English) Zbl 1120.68052

Summary: In quantum computational logic meanings of sentences are identified with quantum information quantities: systems of qubits or, more generally, mixtures of systems of qubits. We consider two kinds of quantum computational semantics: (1) a compositional semantics, where the meaning of a compound sentence is determined by the meanings of its parts; (2) a holistic semantics, which makes essential use of the characteristic “holistic” features of the quantum-theoretic formalism. We prove that the compositional and the holistic semantics characterize the same logic.

MSC:

68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
81P68 Quantum computation
03G12 Quantum logic
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