Breakdown of the Classical Description of a Local System

Eran Kot, Niels Grønbech-Jensen, Bo M. Nielsen, Jonas S. Neergaard-Nielsen, Eugene S. Polzik, and Anders S. Sørensen
Phys. Rev. Lett. 108, 233601 – Published 6 June 2012

Abstract

We provide a straightforward demonstration of a fundamental difference between classical and quantum mechanics for a single local system: namely, the absence of a joint probability distribution of the position x and momentum p. Elaborating on a recently reported criterion by Bednorz and Belzig [Phys. Rev. A 83, 052113 (2011)] we derive a simple criterion that must be fulfilled for any joint probability distribution in classical physics. We demonstrate the violation of this criterion using the homodyne measurement of a single photon state, thus proving a straightforward signature of the breakdown of a classical description of the underlying state. Most importantly, the criterion used does not rely on quantum mechanics and can thus be used to demonstrate nonclassicality of systems not immediately apparent to exhibit quantum behavior. The criterion is directly applicable to any system described by the continuous canonical variables x and p, such as a mechanical or an electrical oscillator and a collective spin of a large ensemble.

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  • Received 14 October 2011

DOI:https://doi.org/10.1103/PhysRevLett.108.233601

© 2012 American Physical Society

Authors & Affiliations

Eran Kot1,*, Niels Grønbech-Jensen2,3, Bo M. Nielsen1,†, Jonas S. Neergaard-Nielsen1,†, Eugene S. Polzik1, and Anders S. Sørensen1

  • 1The Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark
  • 2The Niels Bohr International Academy, The Niels Bohr Institute, Copenhagen DK-2100, Denmark
  • 3Department of Applied Science, University of California, Davis, California 95616, USA

  • *eran.kot@nbi.dk
  • Present address: Department of Physics, Technical University of Denmark, Building 309, DK-2800 Lyngby, Denmark.

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Issue

Vol. 108, Iss. 23 — 8 June 2012

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