A Spectral Identifiability Threshold for Dissipative Rate Recovery from Truncated Liouvillian Spectra
Abstract
Open quantum systems lose energy and phase coherence through different dissipative processes, but these processes can produce overlapping dynamical signatures. The Liouvillian spectrum summarizes how such a system relaxes, yet it is not obvious how much of that spectrum is needed to distinguish the underlying dissipation rates. We study this question for amplitude damping and dephasing in a six-qubit Lindblad model whose spectrum can be derived analytically. We retain only the slowest non-steady spectral modes and ask how many are required before each dissipative rate becomes recoverable. We show that population modes contain no dephasing information, which creates a lower bound of D = 2^n retained modes for uniform dephasing identifiability in the relevant rate regime. The measured recovery threshold reaches this bound at n = 4,5,6, while n = 3 remains above it. At n = 6, least squares achieves a mean joint absolute error of order 10^-9, compared with 4.355 x 10^-4 for four tabular learning methods. Robustness tests show that this advantage weakens when the spectra are perturbed and when a transverse field breaks the commuting structure. These results show that the amount and structure of retained spectral information can determine whether dissipative parameters are recoverable, independently of the estimator used. The present conclusions apply to noise-free simulator spectra rather than measurement-derived spectra.
Related
- Self-Trapping and Liouvillian Spectral Transitions in a Dissipative Bose-Hubbard Dimer
- Interpreting Liouvillian Eigenmodes: Quantized Orbits in Dissipative Systems
- Liouvillian spectral snapshots: A reduced-subspace approach for time-dependent and noisy open quantum systems
- Multi-Threshold Sampling: Local and Global Parameter Identifiability
- Spectral Oscillations and Temporal Meandering of Dissipative Solitons in a Moving Intracavity Phase Potential
BibTeX
@misc{ji2026spectral,
title = {{A Spectral Identifiability Threshold for Dissipative Rate Recovery from Truncated Liouvillian Spectra}},
author = {Yujun Ji and Somyajit Chakraborty},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29302},
eprint = {2608.29302},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29302},
}
RIS
TY - UNPB
TI - A Spectral Identifiability Threshold for Dissipative Rate Recovery from Truncated Liouvillian Spectra
AU - Yujun Ji
AU - Somyajit Chakraborty
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.29302
UR - https://arxiv.org/abs/2608.29302
AB - Open quantum systems lose energy and phase coherence through different dissipative processes, but these processes can produce overlapping dynamical signatures. The Liouvillian spectrum summarizes how such a system relaxes, yet it is not obvious how much of that spectrum is needed to distinguish the underlying dissipation rates. We study this question for amplitude damping and dephasing in a six-qubit Lindblad model whose spectrum can be derived analytically. We retain only the slowest non-steady spectral modes and ask how many are required before each dissipative rate becomes recoverable. We show that population modes contain no dephasing information, which creates a lower bound of D = 2^n retained modes for uniform dephasing identifiability in the relevant rate regime. The measured recovery threshold reaches this bound at n = 4,5,6, while n = 3 remains above it. At n = 6, least squares achieves a mean joint absolute error of order 10^-9, compared with 4.355 x 10^-4 for four tabular learning methods. Robustness tests show that this advantage weakens when the spectra are perturbed and when a transverse field breaks the commuting structure. These results show that the amount and structure of retained spectral information can determine whether dissipative parameters are recoverable, independently of the estimator used. The present conclusions apply to noise-free simulator spectra rather than measurement-derived spectra.
ER -