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Is Information the Key?

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Part of the The Western Ontario Series in Philosophy of Science book series (WONS,volume 78)

Abstract

The difference between classical and quantum information arises because of the different distinguishability properties of classical and quantum pure states: only orthogonal quantum states are reliably distinguishable with zero probability of error. Classical information is that sort of information represented in a set of distinguishable states and so can be regarded as a subcategory of quantum information. The transition from classical to relativistic physics rests on the recognition that space-time structurally different than we thought. In the transition from classical to quantum physics, what we have discovered is that information in the physical sense is structurally different than we thought. The claim about information and quantum mechanics is that the puzzling and seemingly paradoxical features of the theory, including the measurement problem, are to be understood as arising from this structural difference.

Keywords

  • Quantum Correlation
  • Credence Function
  • Deterministic State
  • Hide Variable Theory
  • Stochastic Source

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This chapter is dedicated to Bill Demopoulos , my oldest philosophical friend. We began talking about quantum mechanics in the 1960’s, when it seemed to us that quantum logic was the key. Over the years we have had countless conversations about quantum mechanics. Our positions have evolved, sometimes differently, but at the heart of it there is a continuity.

This is also the title of a paper by Gilles Brassard with similar ideas on quantum information. See (Brassard 2000).

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Notes

  1. 1.

    See (Short and Wehner 2010), where the authors show how to define a general measure of information for a broad class of theories, including nonlocal box theories (see below) that reduces to von Neumann entropy for quantum theories and to Shannon entropy for classical theories.

  2. 2.

    It is convenient to change units here to relate the probability to the usual expression for the Clauser-Horne-Shimony-Holt correlation , where the expectation values are expressed in terms of ±1 values for x and y (corresponding to the relevant observables). Note that ‘outputs same’ or ‘outputs different’ mean the same thing whatever the units, so the probabilities \(p\,({\textrm{outputs}}\,{\textrm{same}}\,|\,xy)\) and \(p\,({\textrm{outputs}}\,{\textrm{different}}\,|\,xy)\) take the same values whatever the units, but the expectation value \(\langle xy \rangle\) depends on the units for x and y.

  3. 3.

    A polytope is the analogue of a polygon in many dimensions. A convex set is, roughly, a set such that from any point in the interior it is possible to ‘see’ any point on the boundary.

  4. 4.

    ‘Outputs same’ = parity 0; ‘outputs different’ = parity 1.

  5. 5.

    There is also the ‘many worlds’ option of the Everett interpretation (Saunders et al. 2010). This essentially involves a multiplicity of simplices, one for each ‘world.’

  6. 6.

    Note that Bell ’s objection to decoherence as a solution to the measurement problem (Bell 1990) concerns (rightly) the inadequacy of decoherence as a ‘for all practical purposes’ solution to the first problem. It is not an objection to the second problem.

References

  • Bell, John Stuart. 1964. On the Einstein-Podolsky-Rosen paradox. Physics 1: 195–200. Reprinted in Bell, John Stuart. 1989. Speakable and unspeakable in quantum mechanics. Cambridge: Cambridge University Press.

    Google Scholar 

  • Bell, John Stuart. 1966. On the problem of hidden variables in quantum mechanics. Reviews of Modern Physics 38(3): 447–452. Reprinted in Bell, John Stuart. 1989. Speakable and unspeakable in quantum mechanics. Cambridge: Cambridge University Press.

    CrossRef  Google Scholar 

  • Bell, John Stuart. 1990. Against measurement. Physics World, 8: 33–40. Reprinted in Sixty-two years of uncertainty: historical, philosophical and physical inquiries into the foundations of quantum mechanics, ed. Arthur Miller, 17–31. New York: Plenum.

    Google Scholar 

  • Bohm, David. 1952. A suggested interpretation of quantum theory in terms of ‘hidden’ variables. I and II. Physical Review 85:166–193.

    CrossRef  Google Scholar 

  • Bohr, Niels. 1935. Can quantum-mechanical description of physical reality be considered complete? Physical Review 48:696–702.

    CrossRef  Google Scholar 

  • Born, Max. 1971. The Born-Einstein Letters. London: Walker and Co.

    Google Scholar 

  • Brassard, Gilles. 2000. Quantum foundations in the light of quantum cryptography. Workshop on Quantum foundations in the light of quantum information and cryptography. Université de Montréal, 17–19 May, 2000.

    Google Scholar 

  • Bub, Jeffrey. 2009. Bub-Clifton theorem. In Compendium of quantum physics, eds. D. Greenberger, K. Hentschel, and F. Weinert, 84–86. Berlin and New York: Springer.

    CrossRef  Google Scholar 

  • Clauser, John F., Michael A. Horne, Abner Shimony, and Richard A. Holt. 1969. Proposed experiment to test local hidden-variable theories. Physical Review Letters 23:880–883.

    CrossRef  Google Scholar 

  • Einsten, Albert, Boris Podolosky, and Nathan Rosen. 1935. Can quantum-mechanical description of physical reality be considered complete? Physical Review 47: 777–780.

    CrossRef  Google Scholar 

  • Frigg, Roman, and Carl Hoefer. 2010. Determinism and chance from a Humean perspective. In The present situation in the philosophy of science, eds. Friedrich Stadler, Dennis Dieks, Wenceslao J. González, Stephan Hartmann, Thomas Uebel, and Marcel Weber, 351–372. Berlin and New York: Springer.

    CrossRef  Google Scholar 

  • Ghirardi, Gian-Carlo. 2008. Collapse theories. The Stanford encyclopedia of philosophy (Fall 2008 Edition), ed. Edward N. Zalta. http://plato.stanford.edu/archives/fall2008/entries/qm-collapse/ . Accessed 12 June 2011.

  • Hoefer, Carl. 2007. The third way on objective probability: a sceptic’s guide to objective chance. Mind 116(463): 549–596.

    CrossRef  Google Scholar 

  • Popescu, Sandu, and Daniel Rohrlich. 1994. Quantum non-locality as an axiom. Foundations of Physics 24(3): 379–385.

    CrossRef  Google Scholar 

  • Saunders, Simon, Jonathan Barrett, Adrian Kent, and David Wallace. 2010. Many worlds? Everett, quantum theory, and reality. Oxford: Oxford University Press.

    Google Scholar 

  • Short, Anthony J., and Stephanie Wehner. 2010. Entropy in general physical theories. New Journal of Physics 12: 033023–033057.

    CrossRef  Google Scholar 

  • von Neumann, John. 1955. Mathematical foundations of quantum mechanics. Princeton: Princeton University Press.

    Google Scholar 

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Acknowledgments

This paper was written during the tenure of a University of Maryland RASA semester research award.

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Correspondence to Jeffrey Bub .

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Bub, J. (2012). Is Information the Key?. In: Frappier, M., Brown, D., DiSalle, R. (eds) Analysis and Interpretation in the Exact Sciences. The Western Ontario Series in Philosophy of Science, vol 78. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2582-9_12

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