Deduction, Ordering, and Operations in Quantum Logic

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dc.creatorMegill, Norman D.
dc.creatorPavicic, Mladen
dc.date2001-08-16
dc.date.accessioned2026-07-07T06:02:34Z
dc.date.available2026-07-07T06:02:34Z
dc.descriptionWe show that in quantum logic of closed subspaces of Hilbert space one cannot substitute quantum operations for classical (standard Hilbert space) ones and treat them as primitive operations. We consider two possible ways of such a substitution and arrive at operation algebras that are not lattices what proves the claim. We devise algorithms and programs which write down any two-variable expression in an orthomodular lattice by means of classical and quantum operations in an identical form. Our results show that lattice structure and classical operations uniquely determine quantum logic underlying Hilbert space. As a consequence of our result, recent proposals for a deduction theorem with quantum operations in an orthomodular lattice as well as a substitution of quantum operations for the usual standard Hilbert space ones in quantum logic prove to be misleading. Quantum computer quantum logic is also discussed.
dc.description19 pages; Web page: http://m3k.grad.hr/pavicic
dc.identifierhttps://arxiv.org/abs/quant-ph/0108074
dc.identifierhttp://arxiv.org/abs/quant-ph/0108074
dc.identifierFound. Phys. 32 (2002) 357-378
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/89653
dc.subjectQuantum Physics
dc.subjectMathematical Physics
dc.subjectLogic
dc.subjectQuantum Algebra
dc.titleDeduction, Ordering, and Operations in Quantum Logic
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