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I will discuss two problems: (i) observing measurement-induced collective phenomena, such as the measurement-induced entanglement transition, and (ii) testing the eigenstate thermalization hypothesis, which forms the basis of our understanding of thermalization in isolated many-body quantum systems. In the first case, standard experiments are not scalable because of the need to post-select on sets of measurement outcomes whose probabilities are exponentially small in the number of degrees of freedom. I will show that a different approach, which involves cross-correlating classical and quantum simulations, can be used to determine both upper and lower bounds on measurement-induced entanglement. This result shows that it is possible to efficiently and unambiguously observe measurement-induced collective phenomena. In the second case, a basic issue is that the theory of thermalization in isolated many-body quantum systems is formulated in terms of properties of eigenstates. At finite energy densities, many-body level separations are exponentially small, so in general we need exponential time to resolve eigenstates. I will show how the quantum search algorithm can be used to construct states having inverse polynomial energy width, as well as superpositions of such states. I will then discuss how, using these states, it is possible to formulate a test for violations of ETH that is valid in individual systems. Finally, I will show that detecting a violation of ETH using this test is a Quantum Merlin Arthur (QMA) problem.

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Sam Garratt, UC Berkeley
Seminar Room 0.03, ETP
Contact: Guo-Yi Zhu