Can single photon excitation of two spatially separated modes lead to a violation of Bell inequality via weak-field homodyne measurements?

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