Quantum Matter Seminar

I will discuss the problem of observing quantum collective phenomena which arise from large numbers of measurements. A prominent example is the measurement-induced entanglement transition, a close relative of transitions in the hardness of random circuit sampling. Directly observing these phenomena is difficult because, in order to distinguish the effects of measurement from dephasing, it is necessary to observe the same sets of outcomes multiple times; the time required for this is in general exponentially large in the number of measurements performed. An indirect approach, which avoids this exponential 'post-selection problem', is to construct cross-correlations between experimental data and the results of simulations on classical computers. Developing this idea, I will show how to both upper and lower bound the average post-measurement entanglement entropy without post-selection. This result shows that it is possible to efficiently and unambiguously observe measurement-induced collective phenomena.