Continuously Monitored Quantum Systems beyond Lindblad Dynamics

TL;DR

This paper develops an analytical framework to analyze the probability distribution of observable expectation values in continuously monitored quantum systems beyond Lindblad dynamics, providing insights into quantum trajectories and measurement effects.

Contribution

It introduces a new analytical method to evaluate the distribution of observable expectations in quantum trajectories beyond Lindblad models, with applications to specific quantum systems.

Findings

Analytical evaluation of expectation value distributions over quantum trajectories.

Application to single qubit magnetization measurements.

Application to free hopping particle position measurements.

Abstract

The dynamics of a quantum system, undergoing unitary evolution and continuous monitoring, can be described in term of quantum trajectories. Although the averaged state fully characterises expectation values, the entire ensamble of stochastic trajectories goes beyond simple linear observables, keeping a more attentive description of the entire dynamics. Here we go beyond the Lindblad dynamics and study the probability distribution of the expectation value of a given observable over the possible quantum trajectories. The measurements are applied to the entire system, having the effect of projecting the system into a product state. We develop an analytical tool to evaluate this probability distribution at any time t. We illustrate our approach by analyzing two paradigmatic examples: a single qubit subjected to magnetization measurements, and a free hopping particle subjected to position measurements.