Ultrafast Entanglement Dynamics in Monitored Quantum Circuits

Abstract

Projective measurement, a basic operation in quantum mechanics, can induce seemingly nonlocal effects. In this work, we analyze such effects in many-body systems by studying the non-equilibrium dynamics of weakly monitored quantum circuits, focusing on entanglement generation and information spreading. We find that, due to measurements, the entanglement dynamics in monitored circuits is indeed "faster" than that of unitary ones in several ways. Specifically, we find that a pair of well-separated regions can become entangled in a time scale ${\ell }^{2/3}$, sub-linear in their distance $\ell$. For the case of Clifford monitored circuits, this originates from super-ballistically growing stabilizer generators of the evolving state. In addition, we find initially local information can spread super-ballistically as $t^{3/2}$. Furthermore, by viewing the dynamics as a dynamical encoding process, we show that the super-ballistic growing length scale relates to an encoding time that is sublinear in system size. To quantify the information dynamics, we develop a formalism generalizing operator spreading to non-unitary dynamics, which is of independent interest.

arXiv comment19 pages

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• Quantum complexity phase transitions in monitored random circuits
• Boundary transitions from a single round of measurements on gapless quantum states
• The Fate of Entanglement
• Random Quantum Circuits with Time-Reversal Symmetry
• Exact, Average, and Broken Symmetries in a Simple Adaptive Monitored Circuit
• Dynamically generated concatenated codes and their phase diagrams
• Quantum conditional mutual information as a probe of measurement-induced entanglement phase transitions
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