Negative quasiprobability trajectories for Bell-diagonal states under local decoherence
Abstract
The fluctuation theorem (FT) relates microscopic trajectory distributions to macroscopic averages. Using quasiprobability trajectories, this framework has recently been extended to quantum information dynamics. Despite sharing the form of conventional thermodynamic FTs, information FTs involve quasiprobabilities whose negativity and statistical properties remain poorly understood. In this work, we analytically determine the properties of negative distributions for two-qubit Bell-diagonal states evolving under local dephasing, depolarizing, and amplitude-damping channels, under the fixed local computational basis. We show that the occurrence of negative quasiprobabilities is not determined by the entanglement or Bell nonlocality of the initial state. For these channels, a diagonal-interference decomposition identifies a nonnegative reference contribution and yields channel-dependent interference bounds. More importantly, we prove that quasiprobability distributions containing negative weights can violate Horváth's necessary and sufficient criterion for the Jensen-Steffensen inequality to hold for every continuous convex function, even though the specific exponential Jensen-like relation enforced by the FT and the quantum data-processing inequality remains valid. This trajectory-level contrast with classical stochastic descriptions reveals a distinctive feature of quantum information dynamics that is invisible when only the corresponding average-level information inequalities are considered.
Versions
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BibTeX
@misc{yu2026negative,
title = {{Negative quasiprobability trajectories for Bell-diagonal states under local decoherence}},
author = {Qing Yu and Kun Zhang and Yang-Yang Chen and Xiao-Hui Wang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2608.16358},
eprint = {2608.16358},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.16358},
}
RIS
TY - UNPB
TI - Negative quasiprobability trajectories for Bell-diagonal states under local decoherence
AU - Qing Yu
AU - Kun Zhang
AU - Yang-Yang Chen
AU - Xiao-Hui Wang
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2608.16358
UR - https://arxiv.org/abs/2608.16358
AB - The fluctuation theorem (FT) relates microscopic trajectory distributions to macroscopic averages. Using quasiprobability trajectories, this framework has recently been extended to quantum information dynamics. Despite sharing the form of conventional thermodynamic FTs, information FTs involve quasiprobabilities whose negativity and statistical properties remain poorly understood. In this work, we analytically determine the properties of negative distributions for two-qubit Bell-diagonal states evolving under local dephasing, depolarizing, and amplitude-damping channels, under the fixed local computational basis. We show that the occurrence of negative quasiprobabilities is not determined by the entanglement or Bell nonlocality of the initial state. For these channels, a diagonal-interference decomposition identifies a nonnegative reference contribution and yields channel-dependent interference bounds. More importantly, we prove that quasiprobability distributions containing negative weights can violate Horváth's necessary and sufficient criterion for the Jensen-Steffensen inequality to hold for every continuous convex function, even though the specific exponential Jensen-like relation enforced by the FT and the quantum data-processing inequality remains valid. This trajectory-level contrast with classical stochastic descriptions reveals a distinctive feature of quantum information dynamics that is invisible when only the corresponding average-level information inequalities are considered.
ER -