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Non-Orthomodular Models for Both Quantum Logic and Standard Classical Logic: Repercussions for Quantum Computers | | Mladen Pavicic
; Norman D. Megill
; | | Date: |
27 Jun 1999 | | Journal: | Helv.Phys.Acta 72 (1999) 189-210 | | Subject: | Quantum Physics; Quantum Algebra; Logic | quant-ph math.LO math.QA | | 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. | | Source: | arXiv, quant-ph/9906101 | | Services: | Forum | Review | PDF | Favorites | |
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