Partial Collapse and Ensemble Invariance under Continuous Quantum Measurement
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.
Cite
@article{arxiv.2512.22235,
title = {Partial Collapse and Ensemble Invariance under Continuous Quantum Measurement},
author = {Shalender Singh and Santosh Kumar},
journal= {arXiv preprint arXiv:2512.22235},
year = {2026}
}
Comments
24 pages, 2 figures