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Non-signalling Theories and Generalized Probability

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Abstract

We provide mathematically rigorous justification of using term probability in connection to the so called non-signalling theories, known also as Popescu’s and Rohrlich’s box worlds. No only do we prove correctness of these models (in the sense that they describe composite system of two independent subsystems) but we obtain new properties of non-signalling boxes and expose new tools for further investigation. Moreover, it allows strightforward generalization to more complicated systems.

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Notes

  1. In the famous list of Hilbert problems [11], axiomatic treatment of probability was the most important task of the 6th problem: Mathematical Treatment of the Axioms of Physics.

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Acknowledgments

This work was supported by the grant from the John Templeton Foundation.

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Authors and Affiliations

  1. Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668, Warsaw, Poland

    Tomasz I. Tylec & Marek Kuś

  2. Faculty of Physics, University of Warsaw, Pasteura 5, 02-093, Warsaw, Poland

    Jacek Krajczok

  3. Institute of Theoretical Physics and Astrophysics, University of Gdańsk, ul. Wita Stwosza 57, 80-308, Gdańsk, Poland

    Tomasz I. Tylec

Authors
  1. Tomasz I. Tylec
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  2. Marek Kuś
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  3. Jacek Krajczok
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Correspondence to Tomasz I. Tylec.

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Tylec, T.I., Kuś, M. & Krajczok, J. Non-signalling Theories and Generalized Probability. Int J Theor Phys 55, 3832–3842 (2016). https://doi.org/10.1007/s10773-016-3013-z

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  • DOI: https://doi.org/10.1007/s10773-016-3013-z

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