Year: 2026
Type: article
Abstract: We investigate the behavior of quantum trajectories conditioned on measurement outcomes. Under a condition related to the absence of so-called dark subspaces, Kümmerer and Maassen showed that such trajectories almost surely purify in the long run. An alternative, simple proof of this result is first provided using Lyapunov methods. The result is then strengthened by showing that purification occurs at an exponential rate in expectation, again via a Lyapunov approach. The quantum filter stability problem is then considered: two trajectories are propagated under the same measurement record—one from the true initial state, the other from an arbitrary initial guess—and it is shown that the estimated trajectory converges exponentially fast to the true one. This quantifies the rate at which information about the current state is progressively revealed through the measurement process.
Institutions: University of Nottingham, Université Paris-Saclay
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,325
Awards: Iterative Generation of New quantum states of light for quantum Information processing, Statistical theory of controlled quantum dynamics, G3010527862, G3580386859, Novel non-equilibrium states of matter in periodically driven spin systems: from time crystals to integrated thermal machines, Estimation and control of open quantum systems
OpenAlex ID: W7211953358