LAUSR

Leggett-Garg (LG) tests for macrorealism were originally designed to explore quantum coherence on the macroscopic scale. Interference experiments and systems modelled by harmonic oscillators provide useful examples of situations in which macroscopicity has been approached experimentally and may be turned into LG tests with a dichotomic variable Q by simple partitionings of a continuous variable such as position. Applying this approach to the double-slit experiment in which a measurement at the slits and screen are considered, we find that LG violations are always accompanied by destructive interference. The converse is not true in general and we find that there are non-trivial regimes in which there is destructive interference but the two-time LG inequalities are satisfied which implies that it is in fact often possible to assign (indirectly determined) probabilities for the interferometer paths. Similar features have been observed in recent work involving a LG analysis of a Mach-Zehnder interferometer and we compare with those results. We also compare with the related problem in which a more direct determination of the paths is carried out using a variable-strength measurement at the slits and the resulting deterioration of the interference pattern is examined. We extend the analysis to the triple-slit experiment. We find examples of some surprising relationships between LG inequalities and NSIT conditions that do not exist for dichotomic variables, including a violation of the Luders bound. We analyse a two-time LG inequality for the simple harmonic oscillator. We find an analytically tractable example showing a two-time LG violation with a gaussian initial state, echoing recent results of Bose et al (Phys. Rev. Lett. 120, 210402 (2018)).