**Mladen Pavicic ^{1,2} and
Norman D. Megill^{3}
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^{1}Atominstitute of the Austrian Universities,
Schüttelstraße 115, A-1020 Wien, Austria; pavicic@ati.ac.at
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^{2}
Department of Mathematics, University of Zagreb,
GF, Kaciceva 26, POB-217, HR-10001 Zagreb, Croatia;
mpavicic@faust.irb.hr; http://m3k.grad.hr/pavicic
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^{3}
Locke Lane, Lexington, MA 02173, U. S. A.; nm@alum.mit.edu
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Abstract.
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.
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PACS numbers: 03.65.Bz, 02.10.By, 02.10.Gd
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**Keywords: ** quantum logic, orthomodular lattices,
quantum computation, modus ponens, distributivity, classical logic.

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