publication . Article . Preprint . 2015

Quantum Logic and Quantum Reconstruction

Allen Stairs;
Open Access
  • Published: 22 Jan 2015 Journal: Foundations of Physics, volume 45, pages 1,351-1,361 (issn: 0015-9018, eissn: 1572-9516, Copyright policy)
  • Publisher: Springer Science and Business Media LLC
Abstract
Quantum logic understood as a reconstruction program had real successes and genuine limitations. This paper offers a synopsis of both and suggests a way of seeing quantum logic in a larger, still thriving context.
Persistent Identifiers
Subjects
ACM Computing Classification System: Hardware_LOGICDESIGNGeneralLiterature_MISCELLANEOUSComputerSystemsOrganization_MISCELLANEOUS
free text keywords: General Physics and Astronomy, Quantum Physics, Quantum process, Open quantum system, Quantum technology, Quantum error correction, Mathematics, Theoretical computer science, Quantum operation, Quantum computer, Quantum information, Quantum mechanics, Quantum network
29 references, page 1 of 2

[1] Constantin Piron. Axiomatique quantique. Helvetica Physica Acta, 37:439- 468, 1964. [OpenAIRE]

[2] H. A. Keller. Ein nicht-klassischer Hilbertscher raum. Zeitschrift, 172:41-49, 1980.

[3] M. P. Sole`r. Characterization of Hilbert spaces with orthomodular spaces. Communications in Algebra, 23:219-243, 1995.

[4] Samuel. S. Holland, Jr. Orthomodularity in infinite dimensions; a theorem of M. Sole`r. Bulletin of the American Mathematical Society, 32(2), 1995.

[5] Itamar Pitowsky. Quantum mechanics as a theory of probability. In William Demopoulos and Itamar Pitowsky, editors, Physical theory and its interpretation: Essay in honor of Jeffrey Bub. Springer, Western Ontario Series in Philosophy of Science, New York, 2006. [OpenAIRE]

[6] Erwin Schro¨dinger. Discussion of probability relations between separated systems. Proceedings of the Cambridge Philosophical Society, 31:555-563, 1935.

[7] Allen Stairs. On the logic of pairs of quantum systems. Synthese, 56:47-60, 1983.

[8] B.S. Tsirelson. Quantum generalizations of Bell's inequality. Letters in Mathematical Physics, 4:93-100, 1980.

[9] Sandu Popescu and Daniel Rohrlich. Quantum nonlocality as an axiom. Foundations of Physics, 24:379, 1994. [OpenAIRE]

[10] Allen Stairs and Jeffrey Bub. Correlations, contextuality and quantum logic. Journal of Philosophical Logic, 42:483-499, 2013.

[11] Samuel S. Holland, Jr. The current interest in orthomodular lattices. In J. C. Abbott, editor, Trends in Lattice Theory, pages 41-126. Van Nostrand Reinhold, New York, 1970. Reprinted in The Logico-Algebraic Approach to Quantum Mechanics, Vol. 1, C.A. Hooker, D. Reidel Publishing Company, Dodrecht (1975), pp. 437-496.

[12] Hans Halvorson and Jeffrey Bub. Can quantum cryptography imply quantum mechanics? Reply to Smolin. arXiv:quant-ph/0412063v1, 2009.

[13] Itamar Pitowsky. Betting on the outcomes of measurements: a Bayesian theory of quantum probability. Studies in History and Philosophy of Modern Physics, 34:395-414, 2003.

[14] A.N. Gleason. Measures on the closed sub-spaces of Hilbert spaces. Journal of Mathematics and Mechanics, 6:885-893, 1957.

[15] J. M. Jauch and Constantin Piron. On the structure of quantal propositional systems. Helvetica Physica Acta, 42:842-848, 1969.

29 references, page 1 of 2
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