Probability in quantum computation and quantum computational logics: a survey

Quantum computation and quantum computational logics give rise to some non-standard probability spaces that are interesting from a formal point of view. In this framework, events represent quantum pieces of information ( qubits , quregisters , mixtures of quregisters ), while operations on events are identified with quantum logic gates (which correspond to dynamic reversible quantum processes). We investigate the notion of Shi–Aharonov quantum computational algebra . This structure plays the role for quantum computation that is played by σ-complete Boolean algebras in classical probability theory.

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