Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a possible pure state of a compound quantum system. The generalization to mixed states, which might be useful to analyse entanglement-phenomena, is due to Gudder. Quantum computational logics represent non standard examples of unsharp quantum logic, where the non-contradiction principle is violated, while conjunctions and disjunctions are strongly non-idempotent. In this framework, any sentence of the language gives rise to a quantum tree: a kind of quantum circuit that transforms the quregister associated to the atomic subformulas of the sentence into the quregister associated to the sentence.
CITATION STYLE
Chiara, M. L. D., Giuntini, R., & Leporini, R. (2003). Quantum Computational Logics: A Survey (pp. 229–271). https://doi.org/10.1007/978-94-017-3598-8_9
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