Monitored Qubit Dynamics Enable Mapping to Classical Run-and-Tumble Particle Systems

The behaviour of quantum systems under constant monitoring represents a fundamental challenge in physics, and recent work by Aritra Kundu from the University of Luxembourg and colleagues sheds new light on this complex process. The team investigates how continuous measurement and feedback influence the dynamics of a qubit, revealing a surprising connection to the behaviour of classical ‘Run-and-Tumble’ particles. This research demonstrates that the quantum system’s behaviour can be accurately described using concepts from the study of active matter, specifically the interplay between propulsion and confinement, and establishes a statistically equivalent relationship between quantum measurement and the movement of these classical particles. The findings offer a new framework for understanding non-equilibrium quantum systems and provide insights into the emergence of complex behaviours in monitored quantum devices.

The research investigates the persistent Run-and-Tumble Particle (RTP) in a bounded one-dimensional domain, allowing application of analytical results from classical active matter to derive an approximate non-equilibrium steady-state (NESS) distribution for a monitored quantum system.

Qubit Dynamics Mirror Active Matter Behaviour

This work demonstrates a surprising connection between the dynamics of a qubit undergoing continuous measurement and the behaviour of a classical “run-and-tumble particle,” a model commonly used to describe active matter. Scientists mapped the quantum evolution of the qubit to the dynamics of this classical particle within a confined space, revealing a shared mathematical structure. This mapping allows researchers to apply analytical results from the well-studied field of active matter to understand the complex behaviour of the monitored quantum system. Experiments revealed that the interplay between coherent driving of the qubit and the measurement-induced feedback creates a rich, non-equilibrium steady-state distribution exhibiting a transition analogous to the Zeno, anti-Zeno effect, where strong measurement can “freeze” quantum evolution, while weak measurement allows it to proceed, and this transition statistically mirrors the trapping of an active particle due to its propulsion velocity.

The team derived an equation governing the steady-state distribution, ensuring physically realistic probability densities with reflective boundaries. Analysis of the classical run-and-tumble particle model showed that the stationary probability density is a superposition of exponential modes, perfectly matching numerical simulations. In the low-diffusion limit, the probability density combines a smooth exponential bulk with finite masses at the boundaries, reminiscent of non-Hermitian skin effects. Furthermore, the mean first passage time to the boundary, a measure of how quickly the particle reaches the edge of its confined space, aligns between predictions from the run-and-tumble model and numerical simulations of the quantum system, validating the effective description in the high-noise limit. This breakthrough delivers a novel perspective on quantum measurement, interpreting the Quantum Zeno effect as a form of active transport and opening new avenues for understanding and controlling quantum systems.

Qubit Dynamics Mirror Active Particle Behaviour

This research establishes a connection between the dynamics of a continuously monitored qubit subjected to feedback and the behaviour of a persistent run-and-tumble particle confined to a limited space. By mapping the quantum system onto a classical active matter model, the team derived an approximate distribution describing the qubit’s state, revealing a correspondence between measurement-induced transitions in the qubit and motility-induced transitions observed in active particles. Specifically, the Quantum Zeno effect, where frequent measurement can suppress a quantum system’s evolution, is understood as a form of trapping analogous to that experienced by an active particle in a confined environment. The findings demonstrate that tools developed for studying non-equilibrium statistical mechanics, particularly those used to analyse run-and-tumble particles, offer a valuable framework for characterizing the statistics of quantum trajectories. This approach provides a physical interpretation of the Quantum Zeno effect, linking it to the suppression of coherent motion caused by measurement, mirroring the confinement experienced by an active particle.