Three-fold way of entanglement dynamics in monitored quantum circuits

TL;DR

This paper explores how different random matrix ensembles influence entanglement dynamics in monitored quantum circuits, revealing a three-fold classification of entanglement transition behaviors based on Dyson's ensembles.

Contribution

It introduces a comprehensive analysis of entanglement transitions across Dyson's circular ensembles, combining exact random-matrix theory with numerical simulations to deepen understanding of measurement effects.

Findings

Distinct entanglement transition behaviors for CUE, COE, and CSE ensembles.

Analytical expressions for entanglement generated by gates in different ensembles.

Insights into the interplay between entanglement generation and measurement-induced reduction.

Abstract

We investigate the measurement-induced entanglement transition in quantum circuits built upon Dyson's three circular ensembles (circular unitary, orthogonal, and symplectic ensembles; CUE, COE and CSE). We utilise the established model of a one-dimensional circuit evolving under alternating local random unitary gates and projective measurements performed with tunable rate, which for gates drawn from the CUE is known to display a transition from extensive to intensive entanglement scaling as the measurement rate is increased. By contrasting this case to the COE and CSE, we obtain insights into the interplay between the local entanglement generation by the gates and the entanglement reduction by the measurements. For this, we combine exact analytical random-matrix results for the entanglement generated by the individual gates in the different ensembles, and numerical results for the complete quantum circuit. These considerations include an efficient rephrasing of the statistical entangling power in terms of a characteristic entanglement matrix capturing the essence of Cartan's KAK decomposition, and a general result for the eigenvalue statistics of antisymmetric matrices associated with the CSE.