Information Geometry of Four-Parameter Single-Qutrit States: From Quantum to Semiclassical Geometric Tensors
Abstract
The gap between the classical and quantum Fisher information matrices (CFIM and QFIM) separates what is operationally accessible through measurements from what is intrinsic to a quantum state. In the multiparameter setting, this quantum obstruction is generically not saturable. Motivated by the recently introduced semiclassical geometric tensor (SCGT), we perform an explicit information-geometric study for a class of pure four-parameter single-qutrit states (FPSQSs). These states are probed by a one-parameter family of measurements that interpolates between an uninformative POVM and a sharp projective measurement. We derive closed-form expressions for the CFIM, the quantum geometric tensor (QGT), and the SCGT. We show that the SCGT reproduces the QGT in the projective limit and vanishes in the trivial limit. The real part of the SCGT splits into two terms: the CFIM and an additional nonnegative measurement-transmitted metric in the phase sector. Its imaginary part provides a semiclassical Berry curvature. Its loss relative to the QGT is quantified by a measurement-dependent gap. Our results provide an exactly solvable four-parameter platform for the semiclassical geometric framework. They also clarify how realistic measurements read out the geometric content of quantum states, and how they partially degrade it.
Related
- Quantum Fisher Information in semiclassical magnon systems
- The Shape of Information: Global Information Geometric Limits in Multi-task Quantum Systems
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BibTeX
@misc{xu2026information,
title = {{Information Geometry of Four-Parameter Single-Qutrit States: From Quantum to Semiclassical Geometric Tensors}},
author = {Xue-xiang Xu and Kai-xu Cai and Xue-feng Zhan and Hong-chun Yuan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18558},
eprint = {2609.18558},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18558},
}
RIS
TY - UNPB
TI - Information Geometry of Four-Parameter Single-Qutrit States: From Quantum to Semiclassical Geometric Tensors
AU - Xue-xiang Xu
AU - Kai-xu Cai
AU - Xue-feng Zhan
AU - Hong-chun Yuan
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18558
UR - https://arxiv.org/abs/2609.18558
AB - The gap between the classical and quantum Fisher information matrices (CFIM and QFIM) separates what is operationally accessible through measurements from what is intrinsic to a quantum state. In the multiparameter setting, this quantum obstruction is generically not saturable. Motivated by the recently introduced semiclassical geometric tensor (SCGT), we perform an explicit information-geometric study for a class of pure four-parameter single-qutrit states (FPSQSs). These states are probed by a one-parameter family of measurements that interpolates between an uninformative POVM and a sharp projective measurement. We derive closed-form expressions for the CFIM, the quantum geometric tensor (QGT), and the SCGT. We show that the SCGT reproduces the QGT in the projective limit and vanishes in the trivial limit. The real part of the SCGT splits into two terms: the CFIM and an additional nonnegative measurement-transmitted metric in the phase sector. Its imaginary part provides a semiclassical Berry curvature. Its loss relative to the QGT is quantified by a measurement-dependent gap. Our results provide an exactly solvable four-parameter platform for the semiclassical geometric framework. They also clarify how realistic measurements read out the geometric content of quantum states, and how they partially degrade it.
ER -