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arXiv:2609.36038

Quantum Estimation under Decoherence in Neutrino Oscillations: Quantum Resources, Flavor Accessibility, and Multiparameter Incompatibility

Jilali Loulijat, Abdallah Slaoui, Mohamed Gouighri, Berihu Teklu

quant-phSubmitted Sep 28, 2026• Announced Sep 30, 2026• 0 citations
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Abstract

Neutrino oscillations offer an interferometric setting for open-system dynamics, quantum resources, and parameter estimation. We distinguish two often-conflated statistical families: propagation-basis dephasing uses a survival factor $η_p$ to damp interference before flavor projection, changing flavor probabilities; effective flavor-mode dephasing suppresses only off-diagonal coherence of a single-particle, two-mode state while fixing its populations. For the two-flavor mode state, we derive exact concurrence, entanglement of formation, and local quantum uncertainty, and reduce one-sided projective discord to a one-parameter optimization. For $0<P<1$ and $0<η_m<1$, the QFIM in $(P,χ,η_m)$ is diagonal, with $\mathcal{H}^{\rm mode}_{χχ}=C_{η_m}^2$ and $\mathcal{H}^{\rm mode}_{ξ_mξ_m}=C_{η_m}^2/(1-η_m^2)$, where $ξ_m=-\lnη_m$. For propagation-basis dephasing, basis-matched QFI and flavor FI separate dynamical information loss from measurement inaccessibility for the mixing angle, mass-squared splitting, and dephasing rate. A monochromatic three-flavor benchmark evaluates the mixed-state QFIM, flavor FIM, and SLD incompatibility for $(θ_{23},δ_{\rm CP},ξ_{31},g)$ at DUNE-like, T2HK-like, and ESSnuSB-inspired points. At $Γ_0=10^{-23}\,\mathrm{GeV}$, the fixed-coordinate ratio $\mathcal{F}^{\rm flav}_{δδ}/\mathcal{H}_{δδ}$ is approximately $0.010$, $0.013$, and $0.105$, respectively; all three points show strong $θ_{23}$--$ξ_{31}$ incompatibility. A single-energy flavor measurement supplies only two independent probabilities, so its four-parameter FIM is rank deficient: these diagonal ratios are conditional diagnostics, not joint four-parameter sensitivities. These are state-level information-geometric benchmarks, not event-level sensitivity forecasts.

Comments
21 pages, 9 figures,

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Neutrino oscillations offer an interferometric setting for open-system dynamics, quantum resources, and parameter estimation. We distinguish two often-conflated statistical families: propagation-basis dephasing uses a survival factor ηpη_pηp​ to damp interference before flavor projection, changing flavor probabilities; effective flavor-mode dephasing suppresses only off-diagonal coherence of a single-particle, two-mode state while fixing its populations. For the two-flavor mode state, we derive exact concurrence, entanglement of formation, and local quantum uncertainty, and reduce one-sided projective discord to a one-parameter optimization. For 0<P<10<P<10<P<1 and 0<ηm<10<η_m<10<ηm​<1, the QFIM in (P,χ,ηm)(P,χ,η_m)(P,χ,ηm​) is diagonal, with Hχχmode=Cηm2\mathcal{H}^{\rm mode}_{χχ}=C_{η_m}^2Hχχmode​=Cηm​2​ and Hξmξmmode=Cηm2/(1−ηm2)\mathcal{H}^{\rm mode}_{ξ_mξ_m}=C_{η_m}^2/(1-η_m^2)Hξm​ξm​mode​=Cηm​2​/(1−ηm2​), where ξm=−ln⁡ηmξ_m=-\lnη_mξm​=−lnηm​. For propagation-basis dephasing, basis-matched QFI and flavor FI separate dynamical information loss from measurement inaccessibility for the mixing angle, mass-squared splitting, and dephasing rate. A monochromatic three-flavor benchmark evaluates the mixed-state QFIM, flavor FIM, and SLD incompatibility for (θ23,δCP,ξ31,g)(θ_{23},δ_{\rm CP},ξ_{31},g)(θ23​,δCP​,ξ31​,g) at DUNE-like, T2HK-like, and ESSnuSB-inspired points. At Γ0=10−23 GeVΓ_0=10^{-23}\,\mathrm{GeV}Γ0​=10−23GeV, the fixed-coordinate ratio Fδδflav/Hδδ\mathcal{F}^{\rm flav}_{δδ}/\mathcal{H}_{δδ}Fδδflav​/Hδδ​ is approximately 0.0100.0100.010, 0.0130.0130.013, and 0.1050.1050.105, respectively; all three points show strong θ23θ_{23}θ23​--ξ31ξ_{31}ξ31​ incompatibility. A single-energy flavor measurement supplies only two independent probabilities, so its four-parameter FIM is rank deficient: these diagonal ratios are conditional diagnostics, not joint four-parameter sensitivities. These are state-level information-geometric benchmarks, not event-level sensitivity forecasts.
Neutrino oscillations are at the forefront of advances in Physics beyond the Standard Model. Increasing accuracy in measurements of the neutrino mixing matrix is an important challenge in current experiments. It depends on parameters that do not directly correspond to observables of the neutrino system. This type of estimation problem is handled by Quantum Estimation Theory (QET) via the Fisher Information (FI) and the Quantum Fisher Information (QFI). In this work, we analyze two-flavor neutrino oscillations within the framework of QET. We compute the QFI for the mixing angle θθθ and show that mass measurements are the ones that achieve optimal precision. We also study the FI associated with flavor measurements and show that they are optimized at specific neutrino times-of-flight. Therefore, although the usual population measurement does not realize the precision limit set by the QFI, it can in principle be implemented with the best possible sensitivity to θθθ. We study how these quantifiers relate to the single-particle, mode entanglement. We demonstrate that this form of entanglement does not enhance neither of them. In particular, this shows that in single-particle settings, entanglement is not directly connected with the optimal precision in metrological tasks.
In this work, we analyze two-flavor neutrino oscillations within the framework of quantum estimation theory (QET). We compute the quantum Fischer information (QFI) for the mixing angle [Formula: see text] and show that mass measurements are the ones that achieve optimal precision. We also study the Fischer information (FI) associated with flavor measurements and show that they are optimized at specific neutrino times-of-flight. Therefore, although the usual population measurement does not realize the precision limit set by the QFI, it can in principle be implemented with the best possible sensitivity to [Formula: see text]. We investigate how these quantifiers relate to the single-particle, mode entanglement in neutrino oscillations. We demonstrate that this form of entanglement does not enhance either of them. In particular, our results show that in single-particle settings, entanglement is not directly connected with the enhancement of precision in metrological tasks.
Quantum Fisher information (QFI) bounds state-encoded precision before measurement choice but does not establish identifiability, joint attainability, or detector sensitivity. We develop an operational framework for three-flavor oscillations that separates state, measurement, and reconstructed-event information. At fixed baseline, energy, source flavor, and matter profile, the propagated state is a pure qutrit, so its six-coordinate QFI has rank at most four. Resolved broadband components can restore rank because the aggregate kernel equals the intersection of their active kernels. We analyze joint attainability using quantum curvature, exact pure-state Holevo costs, and numerical primal-dual brackets, and propagate information through flavor projection, detector response, Poisson sampling, and nuisance profiling. An independent implementation of the public DUNE GLoBES configuration reproduces the reference spectra to relative error 3.87×10−163.87\times10^{-16}3.87×10−16 and the profiled likelihood curvature to 3.26×10−63.26\times10^{-6}3.26×10−6. Under the declared scaling and tolerance, its 264-bin event information has numerical rank six at all 176 documented physics points, whereas any four retained rule totals have rank at most four. The weakest record has effective rank five at the declared practical threshold. A conditional likelihood pilot also shows finite-grid overcoverage and dependence on the auxiliary-measurement ensemble. The framework identifies when local quantum or Fisher bounds do not support global experimental-sensitivity claims.
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