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

Abstract

The first one originates from a paper by Tan, Walls and Collett (TWC) [1], in which homodyne-based coincidence intensity measurements with weak coherent light as local auxiliary fields were used to violate the Bell-like inequality of [14].However, the Bell-like inequality in [14] does not rest entirely on Bell's assumptions. Because of that, one can question whether the TWC scheme can be used to violate local realism. For instance, Santos [15] provided an ad hoc local realistic model for the correlation functions considered by TWC. Recently, this line of critique has been reinforced in [16] by presenting a model that reproduces all detection events in the TWC experimental proposal for the range of local oscillator strengths for which the paper [1] reported 'nonlocality' of the single-photon state. In the section III B of this work we show that optical Bell inequalities [17], which must hold for any local realistic description, are not violated for the TWC setup. Thus this case is closed. Still, TWC correlations are interesting in themselves, and variants of this scheme have been realized experimentally in [4] and [11]. In section V we show how to use the CHSH-like inequality of [14] as an entanglement witness.Another idea was put forward by Hardy [2]. He considered states q |00 b1b2 + r √ 2 (|01 b1b2 + |10 b1b2 ), with q = 0

On detecting violation of local realism with photon-number resolving weak-field homodyne measurements

“…Thus, it seems that quantum optical Bell tests with homodyne measurements must involve at least one operational situation in which photon counting replaces weak-field homodyne measurements. This does work also when the local oscillator is almost off, see for the TWC case [27]. On/off situation led to a violation of local realism in Refs.…”

How squeezed states both maximize and minimize the same notion of quantumness

“…Mathematically, all entanglement is created equally while, physically, only certain types of entanglement may be useful [30][31][32][33][34][35]. This has been extensively explored in the literature [36][37][38][39][40][41][42][43][44][45][46], especially some time ago in the context of single-photon entanglement with the vacuum [6,[47][48][49][50][51][52][53][54][55][56][57][58][59][60]; our current focus is not to readdress those questions but to simply ask how much entanglement a state can generate while reserving judgement about the usefulness of such entanglement.…”