Multiparameter Quantum Estimation and Degeneracy Structure in Three-Flavor Neutrino Oscillations
Abstract
We investigate three-flavor neutrino oscillations within the framework of quantum estimation theory using the quantum Fisher information matrix (QFIM). We analyze all six independent elements of the QFIM for the parameters θ23, δCP, and Δm231, together with the corresponding quantum Cramér--Rao bounds and normalized parameter correlations. To connect the intrinsic quantum sensitivity of the neutrino state with experimentally accessible information, we further compare the QFI with the classical Fisher information (CFI) associated with flavor-probability measurements. We find that the difference between the quantum and classical information bounds is strongly dependent on the oscillation parameter and L/E, demonstrating that the efficiency with which the available quantum information is accessed depends on the measurement. We also investigate probability-degenerate solutions in the (θ23,δCP) parameter space. Although different parameter sets can produce identical νμ→νe appearance probabilities at specific L/E values, their corresponding quantum states can remain distinct, as demonstrated by the quantum fidelity. The QFIM differences further reveal distinct local quantum-information geometries for these probability-degenerate solutions, while the corresponding CFIM differences show a parameter and L/E dependent degree of distinguishability accessible through the flavor-probability measurement. Our results demonstrate that QFI and CFI provide complementary information for neutrino parameter estimation, with the QFIM serving as a measurement-independent quantum benchmark and the CFI characterizing the information accessible through a specified measurement.
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BibTeX
@misc{yadav2026multiparameter,
title = {{Multiparameter Quantum Estimation and Degeneracy Structure in Three-Flavor Neutrino Oscillations}},
author = {Bhavna Yadav and Amir Subba and Yu Shi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.30222},
eprint = {2606.30222},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.30222},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Multiparameter Quantum Estimation and Degeneracy Structure in Three-Flavor Neutrino Oscillations
AU - Bhavna Yadav
AU - Amir Subba
AU - Yu Shi
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2606.30222
UR - https://arxiv.org/abs/2606.30222
AB - We investigate three-flavor neutrino oscillations within the framework of quantum estimation theory using the quantum Fisher information matrix (QFIM). We analyze all six independent elements of the QFIM for the parameters θ_23, δ_CP, and Δm^2_31, together with the corresponding quantum Cramér--Rao bounds and normalized parameter correlations. To connect the intrinsic quantum sensitivity of the neutrino state with experimentally accessible information, we further compare the QFI with the classical Fisher information (CFI) associated with flavor-probability measurements. We find that the difference between the quantum and classical information bounds is strongly dependent on the oscillation parameter and L/E, demonstrating that the efficiency with which the available quantum information is accessed depends on the measurement. We also investigate probability-degenerate solutions in the (θ_23,δ_CP) parameter space. Although different parameter sets can produce identical ν_μ→ν_e appearance probabilities at specific L/E values, their corresponding quantum states can remain distinct, as demonstrated by the quantum fidelity. The QFIM differences further reveal distinct local quantum-information geometries for these probability-degenerate solutions, while the corresponding CFIM differences show a parameter and L/E dependent degree of distinguishability accessible through the flavor-probability measurement. Our results demonstrate that QFI and CFI provide complementary information for neutrino parameter estimation, with the QFIM serving as a measurement-independent quantum benchmark and the CFI characterizing the information accessible through a specified measurement.
ER -