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Quantum Logic, Probability, and Information: The Relation with the Bell Inequalities

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Abstract

We study the relation between the Bell inequalities—characteristic of noncontextual hidden variables theories of quantum mechanics—with quantum logic, quantum probability, and quantum information. The emphasis is on clarity and simplicity, although sometimes this implies a lack of mathematical rigor which, I hope, could be resolved without difficulty by the reader.

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References

  • Bell, J. S. (1964). Physics 1, 195.

    Google Scholar 

  • Bell, J. S. (1966). Reviews of Modern Physics 38, 447.

    Google Scholar 

  • Bell, J. S. (1987). Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press, Cambridge, UK.

    Google Scholar 

  • Birckhoff, G. and von Neumann, J. (1936). Annals of Mathematics 37, 823. Reprinted in Ref. 10.

    Google Scholar 

  • Clauser, J. F. and Horne, M. A. (1974). Physical Review of D 10, 526.

    Google Scholar 

  • Clauser, J. F., Horne, M. A., Shimony, A., and Holt, R. A. (1974). Physical Review Letters 23, 880.

    Google Scholar 

  • Einstein, A., Podolsky, B., and Rosen, N. (1935). Physical Review 47, 777.

    Google Scholar 

  • Gleason, A. M. (1957). Journal of Mathematical Mechenics 6, 885.

    Google Scholar 

  • Hooker, C. A. (Ed.)(1975, 1979). The Logico-Algebraic Approach to Quantum Mechanics, Vols. I and II, Reidel, Dordrecht, The Netherlands.

    Google Scholar 

  • Horodecki, R., Horodecki, P., and Horodecki, M. (1996). Physical Review Letters A 210, 377.

    Google Scholar 

  • Horodecki, R. and Horodecki, M. (1996). Physical Review A 54, 1838.

    Google Scholar 

  • Kochen, S. and Specker, E. P. (1967). Journal of Mathematical Mechenics 17, 59.

    Google Scholar 

  • Santos, E. (1986). Physical Letters A 115, 363.

    Google Scholar 

  • von Neumann, J. (1955). Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, NJ (German original 1932).

    Google Scholar 

  • Wheeler, J. A. and Zurek, W. (Eds.) (1983). Quantum Mechanics and Measurement, Princeton University Press, Princeton, NJ.

    Google Scholar 

Download references

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Authors and Affiliations

  1. Departamento de Física, Universidad de Cantabria, Santander, Spain

    Emilio Santos

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  1. Emilio Santos
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Santos, E. Quantum Logic, Probability, and Information: The Relation with the Bell Inequalities. International Journal of Theoretical Physics 42, 2545–2555 (2003). https://doi.org/10.1023/B:IJTP.0000005974.87479.ea

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  • DOI: https://doi.org/10.1023/B:IJTP.0000005974.87479.ea

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