Universal first-passage time statistics for quantum diffusion

TL;DR

This paper provides an exact, universal solution for quantum first-passage time statistics in quantum diffusion driven by measurement noise, revealing insights into decoherence-free subspaces and quantum information processing.

Contribution

It introduces a universal analytical expression for quantum first-passage time distribution that is independent of system specifics, extending classical diffusion concepts to quantum systems.

Findings

First-passage time distribution is universal and system-independent.

Measurement noise can trap quantum systems in decoherence-free subspaces.

Framework established for quantum trajectory first-passage statistics.

Abstract

First-passage phenomena play a fundamental role in classical stochastic processes. We here exactly solve a quantum first-passage time problem for quantum diffusion driven by measurement noise, a generalization of classical Brownian motion. Such continuous monitoring may trap the measured quantum system in a decoherence-free subspace, a fraction of the available state space that is isolated from the surroundings, and thus plays an important role in quantum information science. We analytically determine the first-passage time distribution, whose form neither depends on the system Hamiltonian nor on the measurement operator, and is therefore universal. These results provide a general framework to investigate the first-passage statistics of diffusive quantum trajectories.