The rate of purification of quantum trajectories

• URL: http://arxiv.org/abs/2601.14023v1
• Date: Tue, 20 Jan 2026 14:44:12 GMT
• Title: The rate of purification of quantum trajectories
• Authors: Maël Bompais, Nina H. Amini, Juan P. Garrahan, Mădălin Guţă,
• Abstract summary: We show that quantum trajectories conditioned on measurement outcomes purify in the long run.<n>We also address the quantum state estimation problem by propagating two trajectories under the same measurement record.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 had shown that such trajectories almost surely purify in the long run. In this article, we first present a simple alternative proof of this result using Lyapunov methods. We then strengthen the conclusion by proving that purification actually occurs at an exponential rate in expectation, again using a Lyapunov approach. Furthermore, we address the quantum state estimation problem by propagating two trajectories under the same measurement record--one from the true initial state and the other from an arbitrary initial guess--and show that the estimated trajectory converges exponentially fast to the true one, thus quantifying the rate at which information is progressively revealed through the measurement process.

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