Comment on `Single particle nonlocality with completely independent reference states'

Abstract

We comment on the purported violation of local realism, by a single photon induced correlations between homodyne detectors, which one can find in: New J. Phys. 10, 113024 (2008), [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. I. INTRODUCTIONRef. [1] seems to be the first work to show that a single photon in a superposition of being in one or another exit of a 50-50 beamsplitter can induce correlations, in homodyne measurements at two spatially separated locations, which violate local realism. The work is an element of a long discussion concerning the suggested by Tan, Walls and Collett [2] "non-locality of a single photon". Ref. [1] discusses essentially the same setup as [2], Fig. 1. The difference is that in [2] the local settings of the homodyne measurements were defined by the phases of local oscillator fields, whereas in [1] the settings are defined by transmittivities of the beamsplitters at the final local measurement stations. In both configurations, of [2] and [1], the (moduli of) amplitudes of the local oscillators are fixed, they do not change between settings, and are the same for Alice and Bob. Ref.[2] also claimed a violation of local realism, however this was based on the authors' usage of Bell-like inequalities which involve an additional assumption, except the usual ones needed to derive Bell inequalities. Thus the claim of [2] is unfounded. A final proof of this is given in [3], where one can find an explicit local realistic model for the original Tan-Walls-Collett correlations.The attempt of Ref. [1] does not fall into this trap of incorrect Bell inequalities. They use the good old CHSH ones. Still the violation which they claim does not occur. There is an error in calculation. We show this below.