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There has been a great deal of recent interest in understanding how measurements can influence the dynamics of entanglement in many-body systems. In this talk, I will discuss how long-ranged entanglement can be generated by measuring states prepared by constant-depth 2D quantum circuits. We introduce a new theoretical technique, based on ideas from multi-user quantum Shannon theory, which allows us to establish a rigorous lower bound on the amount of entanglement generated by measurements in this setting. Our method avoids the so-called replica approach--the main tool employed for studying such problems so far--which gives rigorous results only in the simplest of scenarios. Using this technique, we prove that generic (random) 2D shallow circuits produce extensive long-ranged measurement-induced entanglement above some critical depth, even though the pre-measurement state is strictly short-ranged entangled. I will discuss the consequences of this result for the computational complexity of sampling from generic shallow-depth quantum circuits, and for the hardness of contracting random 2D tensor networks. Based on work with Daniel Malz and Wen Wei Ho (arXiv forthcoming)

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Max McGinley, Cambridge
215
Contact: Silvia Pappalardi