Optimal probes for estimating the dephasing of a quantum spin system
Abstract
We investigate the optimal estimation of dephasing in finite-dimensional quantum spin systems. We first discuss some properties of the optimal probe states and present an efficient numerical algorithm to compute the optimal precision in dephasing estimation and identify the optimal probe states. For the dephasing channel arising from Gaussian phase diffusion, a spin cat state is known to be optimal for small dephasing. We analytically determine the range of dephasing strengths over which the cat state remains globally optimal for spins J=1 and J=3/2, and derive upper bounds on its optimality region for larger spins. We then compare numerically several probe states proposed in the literature, showing in particular that the simple class of probes obtained from uniform superpositions of all levels performs near-optimally for stronger dephasing. Finally, we apply our framework to a central-spin model coupled to a nuclear-spin bath, whose dynamics we simulate using the cluster-correlation expansion. Our results show that, while the cat state is optimal for weak Gaussian dephasing, pulse-controlled non-Markovian dynamics can favor states with amplitudes distributed over multiple spin levels, and in some cases the uniform state outperforms the other fixed probes considered. This shows how the choice of probe state depends both on the dephasing strength and on the dynamics.
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BibTeX
@misc{ratini2026optimal,
title = {{Optimal probes for estimating the dephasing of a quantum spin system}},
author = {Leonardo Ratini and Stefano Carretta and Francesco Albarelli},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32724},
eprint = {2610.32724},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32724},
}
RIS
TY - UNPB
TI - Optimal probes for estimating the dephasing of a quantum spin system
AU - Leonardo Ratini
AU - Stefano Carretta
AU - Francesco Albarelli
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32724
UR - https://arxiv.org/abs/2610.32724
AB - We investigate the optimal estimation of dephasing in finite-dimensional quantum spin systems. We first discuss some properties of the optimal probe states and present an efficient numerical algorithm to compute the optimal precision in dephasing estimation and identify the optimal probe states. For the dephasing channel arising from Gaussian phase diffusion, a spin cat state is known to be optimal for small dephasing. We analytically determine the range of dephasing strengths over which the cat state remains globally optimal for spins J=1 and J=3/2, and derive upper bounds on its optimality region for larger spins. We then compare numerically several probe states proposed in the literature, showing in particular that the simple class of probes obtained from uniform superpositions of all levels performs near-optimally for stronger dephasing. Finally, we apply our framework to a central-spin model coupled to a nuclear-spin bath, whose dynamics we simulate using the cluster-correlation expansion. Our results show that, while the cat state is optimal for weak Gaussian dephasing, pulse-controlled non-Markovian dynamics can favor states with amplitudes distributed over multiple spin levels, and in some cases the uniform state outperforms the other fixed probes considered. This shows how the choice of probe state depends both on the dephasing strength and on the dynamics.
ER -