Violations of macroscopic local reality, time and the Q-function

A macroscopic superposition state would appear to be inconsistent with the classical concept of macroscopic realism. Leggett and Garg proposed tests of macroscopic realism based on the validity of a second premise: (macroscopic) noninvasive measureability. Here, we consider tests of macroscopic realism where the second premise is replaced by that of macroscopic locality. Extending results obtained for NOON states [1], we show how one can falsify macroscopic local realism, by using Bell inequalities for cat-states where the choice of polarizer setting is replaced with a choice of time-of-evolution through a nonlinear medium. Different to the original Bell tests, here the outcomes of all relevant measurements are distinct by N bosons at each site, or else are well-separated in phase space. This motivates us to consider a model of reality based on the Q function. In that model, measurement is described by a dynamical interaction where sharp eigenvalues emerge for sufficient amplification, and Bell violations arise, there being backwards-in-time effects arising through negative diffusion terms [2].
[1] M. Thenabadu, G. L. Cheng, T. L. H. Pham, L. V. Drummond, L. Rosales-Zarate, and M. D. Reid, arXiv:1906.04900 [quant-ph] (2019)
[2] P. Drummond and M. D. Reid, arXiv:1909.01798 (2019)