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    Constructing the nonclassical lifetime distribution of two-level systems via quantum reliability

    Yaotian Li1, Y.-M. Du2,*, Wenkui Ding1,†, Zhaoyu Fei1, Libin Fu2, and Xiaoguang Wang1,‡

    • *Contact author: ymdu@gscaep.ac.cn
    • †Contact author: wenkuiding@zstu.edu.cn
    • ‡Contact author: xgwang@zstu.edu.cn

    Phys. Rev. A 112, 032220 – Published 25 September, 2025

    DOI: https://doi.org/10.1103/w98h-hqb2

    Abstract

    To characterize the aging process of quantum devices, the concept of quantum reliability has recently been proposed as a process-based metric that quantifies the duration during which operations remain unaffected by noise. This duration is referred to as the lifetime of a quantum system. In this paper, we investigate the lifetime of a two-level atomic system undergoing spontaneous emission. We construct an exact statistical ensemble of the lifetimes for two-level systems using quantum reliability theory, incorporating comprehensive information such as mean values, fluctuations, and non-classical properties. Notably, we demonstrate that the ensemble exhibits can be represented by a density matrix, which is recorded in the monitoring apparatus by an observation process. Under the Born-Markov approximation, the diagonal elements decay exponentially at a state-dependent rate related to quantum fidelity. Beyond this approximation, the off-diagonal elements arise from interference between radiation pathways and are determined by the first-order coherence of the field. This feature indicates that the off-diagonal elements encode spectral information beyond the Markovian decay rate, suggesting a potential protocol for probing the environmental spectral density using two-level atoms.

    Physics Subject Headings (PhySH)

    Corrections

    12 November, 2025

    Correction: A grant number in the Acknowledgments contained an error and has been fixed.

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