Noisy monitored quantum dynamics of ergodic multi-qubit systems

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.

15 pages, Special Issue 'Advances in Quantum Chaos, Random-Matrix Theory and the Semiclassical Limit: in memory of Fritz Haake' of J. Phys. A

References in corpus (4)

• Critical properties of the measurement-induced transition in random quantum circuits
• Operator scaling dimensions and multifractality at measurement-induced transitions
• Symmetry enriched phases of quantum circuits
• Three-fold way of entanglement dynamics in monitored quantum circuits

Cited by in corpus (8)

• Disordered monitored free fermions
• Random-matrix models of monitored quantum circuits
• A Dyson Brownian motion model for weak measurements in chaotic quantum systems
• Universal Stochastic Equations of Monitored Quantum Dynamics
• Pseudoclassical dynamics of the kicked top
• Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling
• Efficient circular Dyson Brownian motion algorithm
• Hierarchical analytical approach to universal spectral correlations in Brownian Quantum Chaos