dorsal/arxiv
View SchemaNon-Orthomodular Models for Both Quantum Logic and Standard Classical Logic: Repercussions for Quantum Computers
| Authors | Mladen Pavicic, Norman D. Megill |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9906101 |
| URL | https://arxiv.org/abs/quant-ph/9906101 |
| Journal | Helv.Phys.Acta 72 (1999) 189-210 |
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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"abstract": "It is shown that propositional calculuses of both quantum and classical\nlogics are non-categorical. We find that quantum logic is in addition to an\northomodular lattice also modeled by a weakly orthomodular lattice and that\nclassical logic is in addition to a Boolean algebra also modeled by a weakly\ndistributive lattice. Both new models turn out to be non-orthomodular. We prove\nthe soundness and completeness of the calculuses for the models. We also prove\nthat all the operations in an orthomodular lattice are five-fold defined. In\nthe end we discuss possible repercussions of our results to quantum\ncomputations and quantum computers.",
"arxiv_id": "quant-ph/9906101",
"authors": [
"Mladen Pavicic",
"Norman D. Megill"
],
"categories": [
"quant-ph",
"math.LO",
"math.QA"
],
"journal_ref": "Helv.Phys.Acta 72 (1999) 189-210",
"title": "Non-Orthomodular Models for Both Quantum Logic and Standard Classical Logic: Repercussions for Quantum Computers",
"url": "https://arxiv.org/abs/quant-ph/9906101"
},
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