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

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    104146_1.pdf (609.4Kb)
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    Accepted Manuscript (AM)
    Author(s)
    Higgins, BL
    Palsson, MS
    Xiang, GY
    Wiseman, HM
    Pryde, GJ
    Griffith University Author(s)
    Wiseman, Howard M.
    Higgins, Brendon L.
    Palsson, Matthew S.
    Pryde, Geoff
    Xiang, Guo-Yong
    Year published
    2015
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    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 ...
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    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.
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    Journal Title
    Physical Review A - Atomic, Molecular, and Optical Physics
    Volume
    91
    Issue
    1
    DOI
    https://doi.org/10.1103/PhysRevA.91.012113
    Copyright Statement
    © 2015 American Physical Society. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.
    Subject
    Quantum Physics not elsewhere classified
    Mathematical Sciences
    Physical Sciences
    Chemical Sciences
    Publication URI
    http://hdl.handle.net/10072/101297
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    • Journal articles

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