In: Mathematica Slovaca, vol. 54, no. 1
Gianpiero Cattaneo - Maria Luisa Dalla Chiara - Roberto Giuntini - Roberto Leporini
Quantum Computational Structures
Year, pages: 2004, 87 - 108
Quantum computation has suggested new forms of quantum logic, called quantum computational logics ([CATTANEO, G.—DALLA CHIARA, M. L.—GIUNTINI, R.—LEPORINI, R.: An unsharp logic from quantum computation. e@-print: quant-ph/0201013]). The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, representing a possible pure state of a compound physical system, whose associated Hilbert space is an $n$@-fold tensor product $\bigotimesn \Bbb C2$. The generalization to density operators, which might be useful to analyse entanglement-phenomena, is due to [GUDDER, S.: Quantum computational logic. Preprint]. In this paper we study structural properties of density operators systems, where some basic quantum logical gates are defined. We introduce the notions of standard reversible and standard irreversible quantum computational structure. We prove that the second structure is isomorphic with an algebra based on a particular set of complex numbers.
How to cite:
Cattaneo, G., Dalla Chiara, M., Giuntini, R., Leporini, R. 2004. Quantum Computational Structures. In Mathematica Slovaca, vol. 54, no.1, pp. 87-108. 0139-9918.
Cattaneo, G., Dalla Chiara, M., Giuntini, R., Leporini, R. (2004). Quantum Computational Structures. Mathematica Slovaca, 54(1), 87-108. 0139-9918.