Exponentially fast selection of sectors for quantum trajectories beyond non demolition measurements
Mathematical Physics
2025-07-14 v2 math.MP
Quantum Physics
Abstract
We show that, in long time, quantum trajectories select an invariant subspace of the Hilbert space of the system being indirectly measured. This selection is shown to be exponentially fast in an almost sure sense and in average. This result generalizes a known result for non demolition measurements to arbitrary repeated indirect measurements. Our proofs are based on the introduction of a deformation of the original instrument to an equivalent one with a unique invariant state.
Keywords
Cite
@article{arxiv.2407.18864,
title = {Exponentially fast selection of sectors for quantum trajectories beyond non demolition measurements},
author = {Tristan Benoist and Linda Greggio and Clément Pellegrini},
journal= {arXiv preprint arXiv:2407.18864},
year = {2025}
}
Comments
Revised version of the article incorporating a clearer definition of 'sector', following a suggestion from an anonymous reviewer