Difference between revisions of "Quantum Logic"
From MgmtWiki
(→Context) |
|||
| Line 3: | Line 3: | ||
==Context== | ==Context== | ||
| + | == Relationship to other logics == | ||
| + | Quantum logic embeds into [[linear logic]]<ref name=linear>Vaughan Pratt, "[http://boole.stanford.edu/pub/ql.pdf Linear logic for generalized quantum mechanics]," in ''Work­shop on Physics and Computation (PhysComp '92)'' proceedings. See also the dis­cuss­ion at [[#{{harvid|nLab}}|''n''Lab]], [http://ncatlab.org/nlab/revision/quantum%20logic/42 Revision 42], which cites G.D. Crown, "On some orthomodular posets of vector bundles," ''Journ. of Natural Sci. and Math.'', vol. 15 issue 1-2: pp. 11–25, 1975.</ref> and the [[modal logic]] ''B''.{{sfn|Dalla Chiara|Giuntini|2002}} Indeed, modern logics for the analysis of quantum computation often begin with quantum logic, and attempt to graft desirable features of an extension of classical logic thereonto; the results then necessarily embed quantum logic.{{sfn|Baltag|Smets|2006}}{{sfn|Baltag|Bergfeld|Kishida|Sack|2014}} | ||
| + | |||
| + | The orthocomplemented lattice of any set of quantum propositions can be embedded into a Boolean algebra, which is then amenable to classical logic.<ref>Jeffery Bub and William Demopoulos, "The Interpretation of Quantum Mechanics," in ''[https://archive.org/details/logicalepistemol0000unse Logical and Epistemological Studies in Contemporary Physics]'', Boston Studies in the Philosophy of Science 13, ed. Robert S. Cohen and Marx W. Wartofsky; D. Riedel, 1974. pp. 92-122. DOI: [http://dx.doi.org/10.1007/978-94-010-2656-7 10.1007/978-94-010-2656-7]. {{ISBN|978-94-010-2656-7}}.</ref> | ||
==References== | ==References== | ||
* Also see the wiki page on [[Quantum Mechanics]] | * Also see the wiki page on [[Quantum Mechanics]] | ||
[[Category: Physics]] | [[Category: Physics]] | ||
Revision as of 17:29, 17 December 2024
Full Title or Meme
The structure of experimental tests in classical mechanics forms a Boolean algebra, but the structure of experimental tests in quantum mechanics forms a much more complicated structure.
Context
Relationship to other logics
Quantum logic embeds into linear logic[1] and the modal logic B.{{#invoke:Footnotes|sfn}} Indeed, modern logics for the analysis of quantum computation often begin with quantum logic, and attempt to graft desirable features of an extension of classical logic thereonto; the results then necessarily embed quantum logic.{{#invoke:Footnotes|sfn}}{{#invoke:Footnotes|sfn}}
The orthocomplemented lattice of any set of quantum propositions can be embedded into a Boolean algebra, which is then amenable to classical logic.[2]
References
- Also see the wiki page on Quantum Mechanics
