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 sigma-complete Boolean algebras in classical probability theory.