Using weak values to experimentally determine “negative probabilities” in a two-photon state with Bell correlations

B. L. Higgins, M. S. Palsson, G. Y. Xiang, H. M. Wiseman, and G. J. Pryde
Phys. Rev. A 91, 012113 – Published 20 January 2015

Abstract

Bipartite quantum entangled systems can exhibit measurement correlations that violate Bell inequalities, revealing the profoundly counter-intuitive nature of the physical universe. These correlations reflect the impossibility of constructing a joint probability distribution for all values of all the different properties observed in Bell inequality tests. Physically, the impossibility of measuring such a distribution experimentally, as a set of relative frequencies, is due to the quantum back-action of projective measurements. Weakly coupling to a quantum probe, however, produces minimal back-action, and so enables a weak measurement of the projector of one observable, followed by a projective measurement of a noncommuting observable. By this technique it is possible to empirically measure weak-valued probabilities for all of the values of the observables relevant to a Bell test. The marginals of this joint distribution, which we experimentally determine, reproduces all of the observable quantum statistics including a violation of the Bell inequality, which we independently measure. This is possible because our distribution, like the weak values for projectors on which it is built, is not constrained to the interval [0,1]. It was first pointed out by Feynman that, for explaining singlet-state correlations within “a [local] hidden variable view of nature … everything works fine if we permit negative probabilities.” However, there are infinitely many such theories. Our method, involving “weak-valued probabilities,” singles out a unique set of probabilities, and moreover does so empirically.

  • Figure
  • Figure
  • Figure
  • Received 20 September 2012

DOI:https://doi.org/10.1103/PhysRevA.91.012113

©2015 American Physical Society

Authors & Affiliations

B. L. Higgins1,2, M. S. Palsson1, G. Y. Xiang1,3, H. M. Wiseman1, and G. J. Pryde1,*

  • 1Centre for Quantum Dynamics and Centre for Quantum Computation and Communication Technology, Griffith University, Brisbane 4111, Australia
  • 2Institute for Quantum Computing and Department of Physics & Astronomy, University of Waterloo, Waterloo, ON N2L 3G1, Canada
  • 3Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China

  • *G.Pryde@griffith.edu.au

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 91, Iss. 1 — January 2015

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×