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arXiv:2107.07951 · New Journal of Physics

Comment on ‘Single particle nonlocality with completely independent reference states’

Tamoghna Das, Marcin Karczewski, Antonio Mandarino, Marcin Markiewicz, Bianka Wołoncewicz, Marek Żukowski

Published Mar 1, 2022• 10 citations
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Abstract

Abstract We comment on the purported violation of local realism, by a single photon induced correlations between homodyne detectors, which one can find in: (2008) New J. Phys. 10 113024 [arXiv: 0807.0109 ]. The claim is erroneous, due to a calculational mistake. As the result is the basis of other claims in the paper, they are unsubstantiated.

DOI
10.1088/1367-2630/ac55b1

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Abstract We comment on the purported violation of local realism, by a single photon induced correlations between homodyne detectors, which one can find in: (2008) New J. Phys. 10 113024 [arXiv: 0807.0109 ]. The claim is erroneous, due to a calculational mistake. As the result is the basis of other claims in the paper, they are unsubstantiated.
We describe a scheme to demonstrate the nonlocal properties of a single particle by showing a violation of Bell's inequality. The scheme is experimentally achievable as the only inputs are number states and mixed states, which serve as references to 'keep track of the experiment'. These reference states are created completely independently of one another and correlated only after all the measurement results have been recorded. This means that any observed nonlocality must solely be due to the single particle state. All the techniques used are equally applicable to massive bosonic particles as to photons and as such this scheme could be used to show the nonlocality of atoms.
Abstract Nowadays photon-number resolving weak-field homodyne measurements allow realization of emblematic gedankenexperiments revealing correlations of optical fields. This covers experiments on (a) excitation of a pair of spatial modes by a single photon, and (b) two spatial modes in a weakly squeezed vacuum state, involving constant local oscillator strengths. Proving Bell nonclassicality of such correlations demands measurements of complementary observables. We show that typical arrangement of weak-field homodyne detection with measurement settings defined by phases of local oscillators of constant strength does not provide enough complementarity for confirming Bell nonclassicality. In the case of experiment (a) we provide an exact local hidden variable model restoring all quantum probabilities, whereas in the case of experiment (b) we show that the claims of its nonclassicality are unfounded. A full complementarity of wave aspects vs particle (number) can be achieved in a measurement situation in which respectively the local oscillators are on or off. This is shown to lead to an operational scenario, in the case of both experiments (a) and (b), which reveals indisputable violations of local realism. Such schemes may find possible applications in device-independent quantum protocols.