Action principle for continuous quantum measurement

TL;DR

This paper introduces a stochastic path integral formalism for continuous quantum measurement, allowing analysis of rare events and most-likely quantum trajectories through an action principle framework.

Contribution

It develops a novel phase space path integral approach for continuous quantum measurement, enabling the study of rare events and quantum jumps with boundary conditions.

Findings

Derivation of a phase space path integral for measurement outcomes and quantum states.

Identification of most-likely paths via action extremization.

Analysis of quantum jumps in the Zeno measurement regime.

Abstract

We present a stochastic path integral formalism for continuous quantum measurement that enables the analysis of rare events using action methods. By doubling the quantum state space to a canonical phase space, we can write the joint probability density function of measurement outcomes and quantum state trajectories as a phase space path integral. Extremizing this action produces the most-likely paths with boundary conditions defined by preselected and postselected states as solutions to a set of ordinary differential equations. As an application, we analyze continuous qubit measurement in detail and examine the structure of a quantum jump in the Zeno measurement regime.