We reconsider the all-optical weak homodyne-measurement based experimental schemes aimed at revealing Bell nonclassicality (‘nonlocality’) of a single photon. We focus on the schemes put forward by Tan et al (TWC, 1991) and Hardy (1994). In our previous work we show that the TWC experiment can be described by a local hidden variable model, hence the claimed nonclassicality is apparent. The nonclassicality proof proposed by Hardy remains impeccable. We investigate which feature of the Hardy’s approach is crucial to disclose the nonclassicality. There are consequential differences between TWC and Hardy setups: (i) the initial state of Hardy is a superposition of a single photon excitation with vacuum in one of the input modes of a 50–50 beamsplitter. In the TWC case there is no vacuum component. (ii) In the final measurements of Hardy’s proposal the local settings are specified by the presence or absence of a local oscillator field (on/off). In the TWC case the auxiliary fields are constant, only phases are varied. We show that in Hardy’s setup the violation of local realism occurs due to the varying strength of the local oscillators. Still, one does not need to operate in the fully on/off detection scheme. Thus, the nonclassicality in a Hardy-like setup cannot be attributed to the single-photon state alone. It is a consequence of its interference with the photons from auxiliary local fields. Neither can it be attributed to the joint state of the single photon excitation and the local oscillator modes, as this state is measurement setting dependent. Despite giving spurious violations of local realism, the TWC scheme can serve as an entanglement indicator, for the TWC state. Nevertheless an analogue indicator based on intensity rates rather than just intensities overperforms it.

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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.

In the quantum world, correlations can take the form of entanglement which is known to be monogamous. In this Letter we show that another type of correlation, indistinguishability, is also restricted by some form of monogamy. Namely, if particles A and B simulate bosons, then A and C cannot perfectly imitate fermions. Our main result consists in demonstrating to what extent it is possible.

We present a method to extract M -partie bosonic correlations from an N -partite maximally symmetric state (M < N ) with the help of successive applications of single-boson subtractions. We also propose an experimental photonic setup to implement it that can be done with the present technologies.PACS numbers: