Measurement and feedforward induced entanglement negativity transition

Abstract

We study the interplay between measurement-induced dynamics and conditional unitary evolution in quantum systems. We numerically and analytically investigate commuting random measurement and feedforward (MFF) processes, and find a sharp transition in their ability to generate entanglement negativity as the number of MFF channels varies. We also establish a direct connection between these findings and transitions induced by random dephasing from an environment with broken time-reversal symmetry. In one variant of the problem, we employ free probability theory to rigorously prove the transition’s existence. Furthermore, these MFF processes have dynamic circuit representations that can be experimentally explored on current quantum computing platforms. This work was supported by the Air Force Office of Scientific Research MURI program under Grant No. FA9550-19-1-0399, and the Simons Foundation through a Simons Investigator award (Grant No. 669487). AS was partially supported by a Chicago Prize Postdoctoral Fellowship in Theoretical Quantum Science.