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Probability in quantum computation and quantum computational logics: a survey

Published online by Cambridge University Press:  28 March 2014

MARIA LUISA DALLA CHIARA ,
ROBERTO GIUNTINI  and
GIUSEPPE SERGIOLI
MARIA LUISA DALLA CHIARA
Affiliation:
Dipartimento di Filosofia, Università di Firenze, Firenze, via Bolognese 52, I-50139 Firenze, Italy Email: dallachiara@unifi.it
ROBERTO GIUNTINI
Affiliation:
Dipartimento di Pedagogia, Psicologia, Filosofia, Università di Cagliari, via Is Mirrionis 1, I-09123 Cagliari, Italy Email: giuntini@unica.it; giuseppe.sergioli@gmail.com
GIUSEPPE SERGIOLI
Affiliation:
Dipartimento di Pedagogia, Psicologia, Filosofia, Università di Cagliari, via Is Mirrionis 1, I-09123 Cagliari, Italy Email: giuntini@unica.it; giuseppe.sergioli@gmail.com
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Abstract

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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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