Noisy monitored quantum dynamics of ergodic multi-qubit systems

TL;DR

This paper develops a random-matrix-based statistical framework to analyze noisy monitored quantum dynamics in multi-qubit systems, revealing how measurements influence entanglement and state statistics.

Contribution

It introduces a novel analytical and numerical formalism for understanding the interplay of randomness and measurements in quantum systems, applicable to multiple qubits and dynamics.

Findings

Monitoring conditions the state of the measured qubit.

The formalism accurately describes stationary and time-resolved dynamics.

Comparison with quantum kicked top validates the model.

Abstract

I employ random-matrix methods to set up and solve statistical models of noisy nonunitary dynamics that appear in the context of monitored quantum systems. The models cover a range of scenarios combining random dynamics and measurements of variable strength of one or several qubits. The combined dynamics drive the system into states whose statistics reflect the competition of randomizing unitary evolution and the measurement-induced backaction collapsing the state. These effects are mediated by entanglement, as I describe in detail by analytical results. For the paradigmatic case of monitoring via a single designated qubit, this reveals a simple statistical mechanism, in which the monitoring conditions the state of the monitored qubit, which then imposes statistical constraints on the remaining quantities of the system. For the case of monitoring several qubits with prescribed strength, the developed formalism allows one to set up the statistical description and solve it numerically. Finally, I also compare the analytical results to the monitored dynamics of a quantum kicked top, revealing two regimes where the statistical model either describes the full stationary dynamics, or resolves time scales during particular parts of the evolution.