Mixed State Deep Thermalization under Generic Quantum Errors
Abstract
Pure-state deep thermalization predicts that, after sufficient scrambling, projected ensembles approach universal distributions that contain information beyond the reduced density matrix. In realistic quantum systems, however, noise is unavoidable and the projected states are generally mixed. Whether mixed-state deep thermalization admits an analogous universal limiting distribution has remained unclear. Here we answer this question for quantum dynamics containing local quantum channels, i.e., errors. We show that the late-time mixed-state projected ensemble is completely determined by the normalized Choi state of the error channel and is universal, independent of the microscopic details of the underlying unitary dynamics. We establish this result analytically for dual-unitary circuits, global Haar-random dynamics, and local Haar-random circuits at large local dimension, and verify it numerically in qubit circuits and kicked Ising dynamics. In a solvable setting, we further find exponentially fast convergence to the limiting ensemble. Our results extend deep thermalization to noisy quantum dynamics and establish a direct correspondence between quantum errors and universal random mixed-state ensembles.
Related
- Phase-sensitive quantum-state texture during thermalization of a Dzyaloshinskii-Moriya Heisenberg dimer
- Mixed-state quantum geometry of dense two-color QCD matter
- Wavelength-Uniform Quantum Algorithms for Mixed-State Quantum Dynamics
- Efficient Quantum Algorithm for Mixed-State Quantum Geometry
- Observing mixed-state Uhlmann winding numbers in integrated photonic quantum walks
BibTeX
@misc{yu2026mixed,
title = {{Mixed State Deep Thermalization under Generic Quantum Errors}},
author = {Xie-Hang Yu and Pavel Kos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31580},
eprint = {2610.31580},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31580},
}
RIS
TY - UNPB
TI - Mixed State Deep Thermalization under Generic Quantum Errors
AU - Xie-Hang Yu
AU - Pavel Kos
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31580
UR - https://arxiv.org/abs/2610.31580
AB - Pure-state deep thermalization predicts that, after sufficient scrambling, projected ensembles approach universal distributions that contain information beyond the reduced density matrix. In realistic quantum systems, however, noise is unavoidable and the projected states are generally mixed. Whether mixed-state deep thermalization admits an analogous universal limiting distribution has remained unclear. Here we answer this question for quantum dynamics containing local quantum channels, i.e., errors. We show that the late-time mixed-state projected ensemble is completely determined by the normalized Choi state of the error channel and is universal, independent of the microscopic details of the underlying unitary dynamics. We establish this result analytically for dual-unitary circuits, global Haar-random dynamics, and local Haar-random circuits at large local dimension, and verify it numerically in qubit circuits and kicked Ising dynamics. In a solvable setting, we further find exponentially fast convergence to the limiting ensemble. Our results extend deep thermalization to noisy quantum dynamics and establish a direct correspondence between quantum errors and universal random mixed-state ensembles.
ER -