Naslov
Binary orthologic with modus ponens is either orthomodular or distributive

Autori
Pavičić, Mladen ; Megill, Norman D.

Izvornik
Helvetica Physica Acta (0018-0238) 71 (1998), 6; 610-628

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

Ključne riječi
quantum logic; orthomodular lattices; quantum computation; modus ponens; distributivity; classical logic

Sažetak
We show that binary orthologic becomes either quantum or classical logic when nothing but modus ponens rule is added to it, depending on the kind of the operation of implication used. We also show that in the usual approach the rule characterizes neither quantum nor classical logic. The difference turns out to stem from the chosen valuation on a model of a logic. Thus algebraic mappings of axioms of standard quantum logics would fail to yield an orthomodular lattice if a unary---as opposed to binary---valuation were used. Instead, non-orthomodular nontrivial varieties of orthologic are obtained. We also discuss the computational efficiency of the binary quantum logic and stress its importance for quantum computation and related algorithms.

Izvorni jezik
Engleski

Znanstvena područja
Fizika

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