Partial Collapse and Ensemble Invariance under Continuous Quantum Measurement

TL;DR

This paper demonstrates that in driven-dissipative quantum systems, continuous measurement can cause strong state localization along individual trajectories without altering the overall steady state, revealing a regime of partial collapse.

Contribution

It introduces the concept of measurement-invariant steady states and establishes conditions for their existence, highlighting Liouvillian symmetry as a key mechanism.

Findings

Measurement-induced localization occurs without changing the steady state.

A necessary and sufficient condition for steady-state invariance is derived.

Liouvillian symmetry enforces measurement invariance.

Abstract

Wavefunction collapse is commonly associated with unavoidable physical disturbance of the measured system. Here we show that in driven-dissipative quantum systems, continuous measurement can induce strong trajectory-level collapse while leaving the ensemble-averaged steady state strictly invariant. We identify measurement-invariant steady states whose unconditional density matrix remains unchanged under continuous monitoring, despite pronounced measurement-induced localization in conditioned quantum trajectories. This separation between trajectory-level collapse and ensemble invariance defines a regime of partial collapse, in which measurement-induced localization is continuously counteracted by dissipative dynamics. We derive a necessary and sufficient condition for steady-state invariance under continuous measurement and identify Liouvillian symmetry as a concrete dynamical mechanism enforcing it. Our results clarify the distinction between conditional collapse and physical disturbance in open quantum systems and provide a framework for non-invasive continuous monitoring in driven-dissipative settings.