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Phys. Rev. Lett. 102, 110404 (2009) [4 pages]

Positive Phase Space Transformation Incompatible with Classical Physics

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Wonmin Son1,2,3, Johannes Kofler4,5, M. S. Kim6, Vlatko Vedral1,2,3, and Časlav Brukner4,5
1The School of Physics and Astronomy, University of Leeds, LS2 9JT Leeds, United Kingdom
2Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
3Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117543, Singapore
4Fakultät für Physik, Universität Wien, Boltzmanngasse 5, A-1090 Wien, Austria
5Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Boltzmanngasse 3, A-1090 Wien, Austria
6School of Mathematics and Physics, The Queen’s University, Belfast BT7 1NN, United Kingdom

Received 8 October 2008; published 20 March 2009

Bell conjectured that a positive Wigner function does not allow violation of the inequalities imposed by local hidden variable theories. A requirement for this conjecture is “when phase space measurements are performed.” We introduce the theory-independent concept of “operationally local transformations” which refers to the change of the switch on a local measurement apparatus. We show that two separated parties, performing only phase space measurements on a composite quantum system with a positive Wigner function and performing only operationally local transformations that preserve this positivity, can nonetheless violate Bell’s inequality. Such operationally local transformations are realized using entangled ancillae.

© 2009 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.102.110404
DOI:
10.1103/PhysRevLett.102.110404
PACS:
03.65.Ud, 03.65.Ta, 03.67.−a
 
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