Proposal for a macroscopic test of local realism with phase-space measurements

Abstract

We propose a test of local realism based on correlation measurements of continuum valued functions of positions and momenta, known as modular variables. The Wigner representations of these observables are bounded in phase space and therefore, the associated inequality holds for any state described by a non-negative Wigner function. This agrees with Bell's remark that positive Wigner functions, serving as a valid probability distribution over local (hidden) phase space coordinates, do not reveal non-locality. We construct a class of entangled states resulting in a violation of the inequality and thus truly demonstrate non-locality in phase space. The states can be realized through grating techniques in space-like separated interferometric setups. The non-locality is verified from the spatial correlation data that is collected from the screens. arXiv:1508.04588v2 [quant-ph] 9 Dec 2015

Non-Classical Correlations in n-Cycle Setting

“…The even cycle non-contextuality inequalities can be extended to phase space case quite easily following the work of Arora et al [ 26 ], where the authors provided the phase space extension for . We have already discussed the construction corresponding to the maximal violation of inequality in Equation ( 18 ).…”

“…The quantum violation for the state in Equation ( 40 ) corresponds to the maximum quantum violation i.e., for large N . The experimental implementation of the phase space extension is quite simple and follows directly from the work of Arora et al [ 26 ].…”

“…Note that the even cycle generalisation of CHSH inequality is similar to Braunstein–Caves inequalities [ 25 ], which have been heavily investigated in the literature. For the four cycle case, a simple extension of these even cycle non-contextuality inequalities to the phase space case was provided by Arora et al [ 26 ].…”

“…Following the construction provided by Araújo et al [ 21 ], we discuss the necessary and sufficient condition for the violation of the generalised KCBS inequality in Section 3.4 and necessary condition for the violation of even-cycle generalisation of CHSH inequality in Section 3.4 . Furthermore, we provide a simple phase space extension of even cycle generalisation of CHSH inequality by harnessing the techniques provided by Arora et al [ 26 ].…”

Quantum information processing in phase space: A modular variables approach

“…The separation (1), in modular and integer parts, proved itself useful for the detection of entanglement in spatial interference patterns [17][18][19]. Furthermore, measurements of more general modular variables, namely periodic functions of position and momentum operators, have been used recently in proposals to test the Clauser-Horne-Shimony-Holt (CHSH) [20,21], the Leggett-Garg [22,23] and noncontextuality inequalities [24][25][26]. Later on, in Sec.…”