Naslov
Deduction, Ordering, and Operations in Quantum Logic

Autori
Megill, Norman D. ; Pavičić, Mladen

Izvornik
Foundations of physics (0015-9018) 32 (2002), 3; 357-387

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
orthomodular lattice; quantum logic; quantum conjunction; quantum disjunction; deduction theorem; ordering relation; operation algebras; quantum computer

Sažetak
We show that in quantum logic of closed subspaces of Hilbert space one cannot substitute quantum operations for classical (standard Hilbert space) ones and treat them as primitive operations. We consider two possible ways of such a substitution and arrive at operation algebras that are not lattices what proves the claim. We devise algorithms and programs which write down any two-variable expression in an orthomodular lattice by means of classical and quantum operations in an identical form. Our results show that lattice structure and classical operations uniquely determine quantum logic underlying Hilbert space. As a consequence of our result, recent proposals for a deduction theorem with quantum operations in an orthomodular lattice as well as a substitution of quantum operations for the usual standard Hilbert space ones in quantum logic prove to be misleading. Quantum computer quantum logic is also discussed.

Izvorni jezik
Engleski

Znanstvena područja
Fizika

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