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Information-Theoretic Postulates for Quantum Theory

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Quantum Theory: Informational Foundations and Foils

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 181))

Abstract

Why are the laws of physics formulated in terms of complex Hilbert spaces? Are there natural and consistent modifications of quantum theory that could be tested experimentally? This book chapter gives a self-contained and accessible summary of our paper [New J. Phys. 13, 063001, 2011] addressing these questions, presenting the main ideas, but dropping many technical details. We show that the formalism of quantum theory can be reconstructed from four natural postulates, which do not refer to the mathematical formalism, but only to the information-theoretic content of the physical theory. Our starting point is to assume that there exist physical events (such as measurement outcomes) that happen probabilistically, yielding the mathematical framework of “convex state spaces”. Then, quantum theory can be reconstructed by assuming that (i) global states are determined by correlations between local measurements, (ii) systems that carry the same amount of information have equivalent state spaces, (iii) reversible time evolution can map every pure state to every other, and (iv) positivity of probabilities is the only restriction on the possible measurements.

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Acknowledgments

Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. LM acknowledges support from CatalunyaCaixa.

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Authors and Affiliations

  1. Departments of Applied Mathematics and Philosophy, University of Western Ontario, 1151 Richmond Street, London, ON N6A 5B7, Canada

    Markus P. Müller

  2. Department of Physics and Astronomy, University College London, London, WC1E 6BT, UK

    Lluís Masanes

Authors
  1. Markus P. Müller
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  2. Lluís Masanes
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Corresponding authors

Correspondence to Markus P. Müller or Lluís Masanes .

Editor information

Editors and Affiliations

  1. Department of Computer Science, The University of Hong Kong, Hong Kong, China

    Giulio Chiribella

  2. Perimeter Inst Theoretical Physics , Waterloo, Ontario, Canada

    Robert W. Spekkens

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Müller, M.P., Masanes, L. (2016). Information-Theoretic Postulates for Quantum Theory. In: Chiribella, G., Spekkens, R. (eds) Quantum Theory: Informational Foundations and Foils. Fundamental Theories of Physics, vol 181. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-7303-4_5

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  • DOI: https://doi.org/10.1007/978-94-017-7303-4_5

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  • Online ISBN: 978-94-017-7303-4

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