A Study of Fluctuation Growths of Observables in Open Quantum Systems
Abstract
The rate at which quantum fluctuations of observables can change provides a useful characterization of the dynamical behavior of quantum systems. For closed quantum systems undergoing unitary evolution, previous work has established a general upper bound on the growth rate of the uncertainty of an observable in terms of the standard deviation of its dynamical velocity. This result is closely related to quantum acceleration limits and provides a compact constraint on fluctuation growth. In this work, we will briefly review the closed system results and extend this perspective to open quantum systems, where the state evolves nonunitarily as a consequence of interactions with an environment. The central result is an upper bound on the rate of growth of the uncertainty of an observable that remains valid for general density-matrix dynamics. We develop two complementary derivations. The first introduces a Hermitian pseudo-Hamiltonian describing the local unitary evolution of the eigenvectors of the density matrix. The second, and more general, derivation proceeds directly from the density-matrix derivative and therefore does not require knowledge of the generator of the dynamics. Both approaches lead to the same fluctuation-growth bound. An important practical advantage is that the bound can be evaluated from the observable, the state, and its time derivative without requiring reconstruction of the complete dynamical generator.
Related
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BibTeX
@misc{bahreyni2026study,
title = {{A Study of Fluctuation Growths of Observables in Open Quantum Systems}},
author = {Newshaw Bahreyni and Paul M. Alsing and Carlo Cafaro and Walid Redjem and Christian Corda},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05604},
eprint = {2611.05604},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05604},
}
RIS
TY - UNPB
TI - A Study of Fluctuation Growths of Observables in Open Quantum Systems
AU - Newshaw Bahreyni
AU - Paul M. Alsing
AU - Carlo Cafaro
AU - Walid Redjem
AU - Christian Corda
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05604
UR - https://arxiv.org/abs/2611.05604
AB - The rate at which quantum fluctuations of observables can change provides a useful characterization of the dynamical behavior of quantum systems. For closed quantum systems undergoing unitary evolution, previous work has established a general upper bound on the growth rate of the uncertainty of an observable in terms of the standard deviation of its dynamical velocity. This result is closely related to quantum acceleration limits and provides a compact constraint on fluctuation growth. In this work, we will briefly review the closed system results and extend this perspective to open quantum systems, where the state evolves nonunitarily as a consequence of interactions with an environment. The central result is an upper bound on the rate of growth of the uncertainty of an observable that remains valid for general density-matrix dynamics. We develop two complementary derivations. The first introduces a Hermitian pseudo-Hamiltonian describing the local unitary evolution of the eigenvectors of the density matrix. The second, and more general, derivation proceeds directly from the density-matrix derivative and therefore does not require knowledge of the generator of the dynamics. Both approaches lead to the same fluctuation-growth bound. An important practical advantage is that the bound can be evaluated from the observable, the state, and its time derivative without requiring reconstruction of the complete dynamical generator.
ER -