Observing the effects of measurements in many-body quantum systems without post-selection

How do measurements disentangle complex quantum states? If we measure many degrees of freedom there is a fundamental barrier, the so-called 'post-selection problem', to answering this question in experiment: it is extremely unlikely that we will ever observe the same post-measurement state twice. We show how, through a synthesis of experiment and simulation, resource-efficient probes for the effects of measurement can nevertheless be constructed. These probes are cross-correlations between results obtained from experimental quantum systems and from classical simulations. As an application, we discuss how these quantum-classical observables can be used to verify the dramatic effects that measurements have on critical ground states [arXiv:2207.09476].