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.
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
θ 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
θ. 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.
Measurements of the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) neutrino mixing parameters have entered a precision era, enabling increasingly stringent tests of neutrino oscillations. Within the framework of quantum estimation theory, we investigate whether flavor measurements, the only observables currently accessible experimentally, are optimal for extracting the oscillation parameters. We compute the Quantum Fisher Information (QFI) and the classical Fisher Information (FI) associated with ideal flavor projections for all oscillation parameters, considering accelerator muon (anti)neutrino and reactor electron antineutrino beams propagating in vacuum. Two main results emerge. First, flavor measurements saturate the QFI at the first oscillation maximum for
θ13,
θ23, and
θ12, demonstrating their information-theoretic optimality for these parameters. In contrast, they are far from optimal for
δCP. In particular, only a small fraction of the available information on
δCP is extracted at the first maximum; the sensitivity improves at the second maximum, in line with the strategy of ESS
νSB, a planned facility. Second, the QFI associated with
δCP is approximately one order of magnitude smaller than that of the mixing angles, indicating that the neutrino state intrinsically encodes less information about CP violation. Nevertheless, this quantum bound lies well below current experimental uncertainties, implying that the present precision on
δCP is not fundamentally limited. Our results provide a quantitative framework to disentangle fundamental from practical limitations and establish a benchmark for optimizing future neutrino facilities.
In this work, we studied entanglement and decoherence in neutrino oscillations from a quantum metrology perspective. A summary of the quantum eld theoretic description of neutrinos was done and the main quantum mechanical models were used to analyze the inuence of entanglement and decoherence on the quantum Fisher information related to the mixing angle. We have found that, although in a variety of physical settings there is a positive relationship between entanglement and the quantum Fisher information, this is not the case in the neutrino oscillations scenario. This shows that, at least in single-particle settings, entanglement is not directly related to the optimal estimation in metrological tasks.
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
ηp 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<ηm<1, the QFIM in
(P,χ,ηm) is diagonal, with
Hχχmode=Cηm2 and
Hξmξmmode=Cηm2/(1−ηm2), where
ξm=−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) at DUNE-like, T2HK-like, and ESSnuSB-inspired points. At
Γ0=10−23GeV, the fixed-coordinate ratio
Fδδflav/Hδδ is approximately
0.010,
0.013, and
0.105, respectively; all three points show strong
θ23--
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.
Quantum estimation theory provides ultimate precision bounds on parameter estimation, independent of experimental setups. In this article, we apply this theoretical framework to neutrino oscillations, aiming to clarify some subtle issues and reveal the maximum achievable precision of oscillation parameters. First, taking the example of two-flavor oscillations, we clarify how the quantum Fisher information (QFI) depends on the choice of bases when the basis transformation itself involves the parameters in question. Then, for three-flavor oscillations, we compute the QFI matrix for electron and muon neutrino states in the flavor basis and derive analytical expressions and numerical results for both diagonal and off-diagonal elements. The implications of off-diagonal correlations for multiparameter estimation are discussed, and the quantum Cramér-Rao bounds on the precision of oscillation parameters for typical reactor and long-baseline accelerator neutrino experiments are obtained. Our results establish a theoretical benchmark for the ultimate precision achievable in future neutrino oscillation experiments.
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
Δm312, 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.