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Résumé |
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 describe 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 a recent conjecture about generic (random) 2D shallow circuits followed by measurements: Namely, that above some O(1) critical depth, extensive long-ranged measurement-induced entanglement is produced, even though the pre-measurement state is strictly short-ranged entangled. This result has consequences for the computational complexity of sampling from generic shallow-depth quantum circuits, and for the hardness of contracting random 2D tensor networks |
