Non-Orthomodular Models for Both Quantum Logic and Standard Classical Logic: Repercussions for Quantum Computers
摘要
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.
引用
@article{arxiv.quant-ph/9906101,
title = {Non-Orthomodular Models for Both Quantum Logic and Standard Classical Logic: Repercussions for Quantum Computers},
author = {Mladen Pavicic and Norman D. Megill},
journal= {arXiv preprint arXiv:quant-ph/9906101},
year = {2007}
}
备注
21 pages, AMSLaTeX, to be published in Helvetica Physica Acta, a few typos corrected, Author's URL http://m3k.grad.hr/pavicic