Proposal for testing Einstein's moon using three-time correlations

Quantum mechanics has predicted many counterintuitive phenomena in daily life, and has changed our view of the world. Among such predictions, the existence of a macroscopic object in superposition is especially unbelievable. As Einstein asked, "Do you really believe that the moon exists only when you look at it?". However, recent experimental results on a mesoscopic scale will ultimately require us to dismiss commonsense so-called macroscopic reality. Leggett and Garg applied the Bell scheme for testing local realism to the time evolution of a macroscopic two-state system, and proposed a temporal version of the Bell inequality (the Leggett-Garg (LG) inequality) for testing macroscopic realism. However, as with the Bell inequality, the statistical approach behind this scheme may be less effective in showing clear incompatibility. Here we propose a temporal version of the Greenberger-Horne-Zeilinger (GHZ) scheme without statistical treatment for testing Einstein's moon using three-time correlations.