Anomaly fluctuation theorem for quantum coherence dynamics
Abstract
Quantum coherence is a central resource in quantum information science, yet general frameworks and constraints governing its dynamics remain limited. Although quantum coherence lacks a general monotonicity law, we establish an exact integral fluctuation theorem (FT) for coherence dynamics, formulated in terms of Kirkwood-Dirac (KD) quasiprobability trajectories and valid for arbitrary initial states and dynamics. This integral FT deviates from the standard unit-valued form, and the complex deviation, termed the anomaly, quantifies a weighted overlap between the residual final-state coherence and the coherence generated from the dephased input. The real part of the anomaly yields bounds on coherence change, while its imaginary part constrains the second-order moment of the stochastic coherence change weighted by the imaginary parts of the KD quasiprobabilities. Our results establish general statistical constraints on coherence dynamics, demonstrating the utility and broad applicability of FTs for studying quantum-resource dynamics.
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BibTeX
@misc{zhang2026anomaly,
title = {{Anomaly fluctuation theorem for quantum coherence dynamics}},
author = {Kun Zhang and Hai-Long Shi and Xiao-Hui Wang and Wen-Li Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06632},
eprint = {2609.06632},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06632},
}
RIS
TY - UNPB
TI - Anomaly fluctuation theorem for quantum coherence dynamics
AU - Kun Zhang
AU - Hai-Long Shi
AU - Xiao-Hui Wang
AU - Wen-Li Yang
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06632
UR - https://arxiv.org/abs/2609.06632
AB - Quantum coherence is a central resource in quantum information science, yet general frameworks and constraints governing its dynamics remain limited. Although quantum coherence lacks a general monotonicity law, we establish an exact integral fluctuation theorem (FT) for coherence dynamics, formulated in terms of Kirkwood-Dirac (KD) quasiprobability trajectories and valid for arbitrary initial states and dynamics. This integral FT deviates from the standard unit-valued form, and the complex deviation, termed the anomaly, quantifies a weighted overlap between the residual final-state coherence and the coherence generated from the dephased input. The real part of the anomaly yields bounds on coherence change, while its imaginary part constrains the second-order moment of the stochastic coherence change weighted by the imaginary parts of the KD quasiprobabilities. Our results establish general statistical constraints on coherence dynamics, demonstrating the utility and broad applicability of FTs for studying quantum-resource dynamics.
ER -