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Non-Orthomodular Models for Both Quantum Logic and Standard Classical Logic: Repercussions for Quantum Computers

Mladen Pavicic·Norman D. Megill
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Abstract

It is shown that propositional calculuses of both quantum and classical logics are non-categorical. We find that quantum logic is in addition to an orthomodular lattice also modeled by a weakly orthomodular lattice and that classical logic is in addition to a Boolean algebra also modeled by a weakly distributive lattice. Both new models turn out to be non-orthomodular. We prove the soundness and completeness of the calculuses for the models. We also prove that all the operations in an orthomodular lattice are five-fold defined. In the end we discuss possible repercussions of our results to quantum computations and quantum computers.

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Mladen Pavicic, Norman D. Megill. 1999-09-12. Non-Orthomodular Models for Both Quantum Logic and Standard Classical Logic: Repercussions for Quantum Computers. https://arxiv.org/abs/quant-ph/9906101

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