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Journal of Mathematical Physics / Volume 50 / Issue 4 / QUANTUM MECHANICS (GENERAL AND NONRELATIVISTIC)

J. Math. Phys. 50, 042104 (2009); http://dx.doi.org/10.1063/1.3114986 (11 pages)

Finite de Finetti theorem for conditional probability distributions describing physical theories

Matthias Christandl1 and Ben Toner2

1Department of Applied Mathematics and Theoretical Physics, Centre for Quantum Computation, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom and Arnold Sommerfeld Center for Theoretical Physics, Faculty of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 Munich, Germany
2School of Physics, The University of Melbourne, Victoria 3010, Australia; Centrum voor Wiskunde en Informatica, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands; and Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125, USA

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(Received 27 July 2008; accepted 17 March 2009; published online 15 April 2009)

We work in a general framework where the state of a physical system is defined by its behavior under measurement and the global state is constrained by no-signaling conditions. We show that the marginals of symmetric states in such theories can be approximated by convex combinations of independent and identical conditional probability distributions, generalizing the classical finite de Finetti theorem of Diaconis and Freedman. Our results apply to correlations obtained from quantum states even when there is no bound on the local dimension, so that known quantum de Finetti theorems cannot be used.

© 2009 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. A DISTANCE MEASURE FOR CONDITIONAL PROBABILITY DISTRIBUTIONS
  3. OUR RESULTS
  4. TOWARDS A FINITE DE FINETTI THEOREM FOR THE CONVEX SET FRAMEWORK

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KEYWORDS and PACS

Keywords

Hilbert spaces, random processes, statistical distributions

PACS

  • 05.40.-a

    Fluctuation phenomena, random processes, noise, and Brownian motion

  • 03.65.Ta

    Foundations of quantum mechanics; measurement theory

  • 02.50.Cw

    Probability theory

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3114986

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    P. Diaconis and D. Freedman, Ann. Probab. 8, 745 (1980)JMAPAQ000043000009004537000001.

    R. König and R. Renner, J. Math. Phys. 46, 122108 (2005)JMAPAQ000046000012122108000001.

    C. M. Caves, C. A. Fuchs, and R. Schack, J. Math. Phys. 43, 4537 (2002)JMAPAQ000043000009004537000001.

    H. Barnum, J. Barrett, M. Leifer, and A. Wilce, Phys. Rev. Lett. 99, 240501 (2007).

    C. A. Fuchs, R. Schack, and P. F. Scudo, Phys. Rev. A 69, 062305 (2004).

    T. Eggeling and R. Werner, Phys. Rev. Lett. 89, 097905 (2002).

    P. Hayden, D. Leung, and G. Smith, Phys. Rev. A 71, 062339 (2005).

    J. Barrett, Phys. Rev. A 75, 032304 (2007).


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