Probability bounds on trajectory-level exceedances of quantum speed limits under continuous-measurement feedback
Abstract
We investigate the probability that a conditioned quantum trajectory exceeds an ensemble-derived quantum speed limit (QSL) velocity under continuous measurement-based feedback. Using the finite-time average fidelity velocity, we derive an upper bound on the exceedance probability in terms of its mean and variance. We further obtain state-independent bounds from uniform constraints on the fidelity drift and diffusion, including an exponential concentration bound. For a feedback-controlled qubit, we derive explicit model-specific bounds and show that they are nontrivial in a short-time regime. We also identify a finite-time regime in which the exceedance probability vanishes exactly due to the restricted support of the conditioned dynamics. Monte Carlo simulations confirm the analytical bounds and illustrate their tightness.
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BibTeX
@misc{kobayashi2026probability,
title = {{Probability bounds on trajectory-level exceedances of quantum speed limits under continuous-measurement feedback}},
author = {Kohei Kobayashi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36356},
eprint = {2610.36356},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36356},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Probability bounds on trajectory-level exceedances of quantum speed limits under continuous-measurement feedback
AU - Kohei Kobayashi
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36356
UR - https://arxiv.org/abs/2610.36356
AB - We investigate the probability that a conditioned quantum trajectory exceeds an ensemble-derived quantum speed limit (QSL) velocity under continuous measurement-based feedback. Using the finite-time average fidelity velocity, we derive an upper bound on the exceedance probability in terms of its mean and variance. We further obtain state-independent bounds from uniform constraints on the fidelity drift and diffusion, including an exponential concentration bound. For a feedback-controlled qubit, we derive explicit model-specific bounds and show that they are nontrivial in a short-time regime. We also identify a finite-time regime in which the exceedance probability vanishes exactly due to the restricted support of the conditioned dynamics. Monte Carlo simulations confirm the analytical bounds and illustrate their tightness.
ER -