Quantum resetting in continuous measurement induced dynamics of a qubit

TL;DR

This paper investigates the stochastic dynamics of a continuously monitored qubit, revealing how measurement-induced resetting influences its evolution and providing exact solutions for related stochastic processes.

Contribution

It introduces a detailed analysis of measurement-induced stochastic resetting in a qubit, including exact solutions for the probability distribution evolution.

Findings

Derived analytic distribution of detector events

Identified transitions in the system's dynamics

Provided exact solutions for stochastic resetting processes

Abstract

We study the evolution of a two-state system that is monitored continuously but with interactions with the detector tuned so as to avoid the Zeno affect. The system is allowed to interact with a sequence of prepared probes. The post-interaction probe states are measured and this leads to a stochastic evolution of the system's state vector, which can be described by a single angle variable. The system's effective evolution consists of a deterministic drift and a stochastic resetting to a fixed state at a rate that depends on the instantaneous state vector. The detector readout is a counting process. We obtain analytic results for the distribution of number of detector events and the time-evolution of the probability distribution. Earlier work on this model found transitions in the form of the steady state on increasing the measurement rate. Here we study transitions seen in the dynamics. As a spin-off we obtain, for a general stochastic resetting process with diffusion, drift and position dependent jump rates, an exact and general solution for the evolution of the probability distribution.