We present a quantum-information-theoretic study of three-flavor neutrino oscillations in long-baseline experiments by mapping flavor states to qubit-like representations and quantifying quantum correlations through total concurrence. The local minima of this entanglement measure identify energy regions where the flavor state is closest to separability, enabling cleaner extraction of oscillation parameters. We explain how these local minima offer opportunities for precision measurements and provide insight into the accurate determination of neutrino oscillation parameters. We then propose a strategy to improve parameter extraction by aligning the benchmark oscillation regions of NO$ν$A and T2K with the minimum entanglement achievable in each experiment. This shifts the concurrence minima toward higher-event-count energy regions, leading to tighter constraints and reducing the tension arising from their different energy regimes. For normal ordering, we obtain $(0.581^{+0.0136}_{-0.0150},195^{+38}_{-32}^\circ)$ in the $(\sin^2θ_{23},δ_{\rm CP})$ plane and $(0.580^{+0.0140}_{-0.0153},2.515^{+0.0344}_{-0.0344}\times10^{-3}\,\mathrm{eV}^2)$ in the $(\sin^2θ_{23},Δm^2_{31})$ plane, yielding improved joint constraints. Using GLoBES simulations together with real data, we assess how local minima of quantum correlations influence leptonic CP-violation sensitivity, $θ_{23}$ octant-degeneracy resolution, and mass-ordering determination. Our results show that minimizing entanglement can significantly affect these key sensitivities, highlighting quantum information measures as complementary probes of neutrino flavor oscillations and offering new insight into the role of quantum correlations in precision neutrino physics.
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34 pages, 8 figures, 3 tables. Comments are welcome
We present a quantum-information-theoretic study of three-flavor neutrino oscillations in long-baseline experiments by mapping flavor states to qubit-like representations and quantifying quantum correlations through total concurrence. The local minima of this entanglement measure identify energy regions where the flavor state is closest to separability, enabling cleaner extraction of oscillation parameters. We explain how these local minima offer opportunities for precision measurements and provide insight into the accurate determination of neutrino oscillation parameters. We then propose a strategy to improve parameter extraction by aligning the benchmark oscillation regions of NOνA and T2K with the minimum entanglement achievable in each experiment. This shifts the concurrence minima toward higher-event-count energy regions, leading to tighter constraints and reducing the tension arising from their different energy regimes. For normal ordering, we obtain (0.581^{+0.0136}_{-0.0150},195^{+38}_{-32}^\circ) in the (sin2θ23,δCP) plane and (0.580−0.0153+0.0140,2.515−0.0344+0.0344×10−3eV2) in the (sin2θ23,Δm312) plane, yielding improved joint constraints. Using GLoBES simulations together with real data, we assess how local minima of quantum correlations influence leptonic CP-violation sensitivity, θ23 octant-degeneracy resolution, and mass-ordering determination. Our results show that minimizing entanglement can significantly affect these key sensitivities, highlighting quantum information measures as complementary probes of neutrino flavor oscillations and offering new insight into the role of quantum correlations in precision neutrino physics.
NNumerous neutrino experiments have confirmed the phenomenon of neutrino oscillation, providing direct evidence of the quantum mechanical nature of neutrinos. In this work, we investigate the entanglement properties of neutrino flavor states within the framework of three-flavor neutrino oscillation using two major entanglement measures: entanglement of formation (EOF) and concurrence, utilizing the DUNE experimental setup. Our findings indicate that the maximally entangled state appears between ν μ and ν τ whereas, ν e behaves as a nearly separable state. To further explore the nature of bipartite entanglement, we introduce the concept of the monogamy of entanglement, which allows us to investigate the distinction between genuine three-flavor entanglement and bipartite entanglement. Our analysis confirms that the three-flavor neutrino system forms a bipartite entanglement structure, adhering to the Coffman-Kundu-Wootters (CKW) inequality. Additionally, we implement a minimization procedure to find the best-fit values of the oscillation parameters that correspond to the concurrence minima at the two specific energy points where the concurrence reaches its lowest values. Using these best-fit values, we probe three fundamental unknowns in neutrino oscillation: CP violation sensitivity, neutrino mass hierarchy, and the octant issue of θ 23 , across two distinct energy points. Our results manifest that while the best-fit values obtained through concurrence minimization show slightly reduced sensitivity to CP violation compared to current best-fit values, they exhibit greater sensitivity to the mass hierarchy. Furthermore, the study reveals a maximal mixing angle for the atmospheric sector.
The flavor oscillations in the neutrino system are known to be related to the multimode entanglement of a single particle state. Neutrino oscillations are shown to encompass not only quantum superposition among different mass eigenstates but also a single-particle multimode entanglement in the flavor basis as they propagate. In the framework of three flavor neutrino oscillations, we demonstrate that the measures of entanglement can be expressed in terms of experimentally accessible appearance and disappearance probabilities. We explicitly show here that the genuine tripartite entanglement measure, i.e., the tangle, vanishes identically for all flavors, signifying that a three flavor neutrino system forms a W-type entangled state. Further, we investigate alternative measures of tripartite entanglement like the partial tangle and the concurrence fill, which capture the total sharing of entanglement beyond pairwise correlations. In terms of bipartite and bipartitioned entanglement measures, we derive the symmetric invariant and the concurrence fill, which quantify the distributed entanglement and are completely expressible in terms of flavor transition probabilities. These entanglement measures display distinct energy dependent patterns across the oscillation window, which can be experimentally accessible in the long baseline experiments like DUNE, providing an alternative quantum information perspective on flavor evolution. We use General Long Baseline Experiment Simulator simulations within the DUNE setup to investigate these tripartite entanglement measures in terms of neutrino energy and the length of the baseline. It is observed that, at the point of maximal mixing, these measures show near maximal entanglement between the muon and the tau flavor modes, establishing entanglement monogamy. Within the DUNE setup, the wide band of energy and expected higher sensitivity to C P violation at the second oscillation maximum provide a unique advantage to explore the quantum correlation effects across a broader energy window. Thus, the flavor coherence and C P -phase dependent interference can influence the quantum entanglement measures among neutrino flavor modes, and thereby, such potential new physics effects can be probed in current or future planned neutrino experiments.
Leptonic CP Phase Determination from Fisher Information in NOνA and T2K
The precise determination of the leptonic CP phase δCP remains one of the central objectives of current and future long-baseline (LBL) neutrino oscillation experiments. Quantum estimation theory provides a natural framework to quantify the ultimate precision limits for estimating physical parameters encoded in quantum states. In this work, we employ the quantum Fisher information to investigate how much information about δCP is intrinsically encoded in neutrino states and how efficiently it is extracted in present LBL experiments such as T2K and NOνA. We first analyze the intrinsic quantum sensitivity of neutrino and antineutrino states and demonstrate how matter effects generate a neutrino mass-ordering dependent information structure. To compare the intrinsic information content of the quantum state with the information experimentally accessible through flavor measurements, we compute the event-level Fisher information from reconstructed event spectra using Poisson statistics. We find that both experiments extract only a small fraction of the total information available in the underlying quantum state. This extraction efficiency becomes particularly suppressed near maximally CP-violating regions, where the reconstructed event spectra exhibit reduced sensitivity to small variations in δCP. Our analysis provides a complementary information-theoretic perspective on precise estimation of oscillation parameters in LBL neutrino 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.
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 ESSνSB, 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.
Determination of the leptonic CP-violating phase δCP, the atmospheric mixing angle θ23, and the mass-squared difference Δm312 constitutes a primary objective of current and next-generation long-baseline neutrino experiments. We employ Quantum Fisher Information (QFI) to quantify the maximum information that the neutrino quantum state contains about these oscillation parameters, treating the neutrino as an evolving pure quantum state. Computing the QFI as a function of the baseline-to-energy ratio L/E for benchmark parameter sets from NuFit-6.0, we find distinct sensitivity hierarchies and L/E-dependent structures. Specifically, δCP and θ23 exhibit bimodal QFI profiles with peaks around L/E∼500 and 1500km/GeV, reaching FQ(δCP)∼0.15 and FQ(θ23)∼15, respectively. In contrast, FQ(Δm312) increases rapidly with L/E over the range considered, reaching values of order 107. This hierarchy indicates that, within the considered single-parameter framework, the neutrino state carries substantially greater intrinsic quantum sensitivity to Δm312 than to θ23 or δCP. We further compare the QFI with the classical Fisher information (CFI) obtained from flavor-transition probabilities, showing how much of the available information can be extracted through this specific measurement. For a fixed DUNE baseline, matter effects substantially enhance the QFI for δCP in the few-GeV region, while producing only minor modifications for θ23 and Δm312. These results show that the information available for estimating the three oscillation parameters differs significantly, and that the flavor-probability measurement does not always extract all the information available in the quantum state.