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

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

1999-06-27

arxiv.org/abs/quant-ph/9906101v3

Helv.Phys.Acta 72 (1999) 189-210

Physics

Quantum Physics

21 pages, AMSLaTeX, to be published in Helvetica Physica Acta, a few typos corrected, Author's URL http://m3k.grad.hr/pavicic

Scientific paper

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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