arXiv:2602.16534 · Journal of High Energy Physics

Quantum Estimation Theory Limits in Neutrino Oscillation Experiments

Claudia Frugiuele, Marco G. Genoni, Michela Ignoti, Matteo G. A. Paris

hep-phhep-exquant-phSubmitted Feb 18, 2026• Announced Feb 19, 2026• 0 citations

Abstract

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 $θ_{13}$, $θ_{23}$, and $θ_{12}$, demonstrating their information-theoretic optimality for these parameters. In contrast, they are far from optimal for $δ_{CP}$. In particular, only a small fraction of the available information on $δ_{CP}$ is extracted at the first maximum; the sensitivity improves at the second maximum, in line with the strategy of ESS$ν$SB, a planned facility. Second, the QFI associated with $δ_{CP}$ 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 $δ_{CP}$ 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.

Journal reference: Journal of High Energy Physics 2026, 218 (2026)
DOI: 10.1007/JHEP08(2026)218
Comments: 21 pages, 11 figures

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arXiv:2602.16534 · Journal of High Energy Physics

Quantum Estimation Theory Limits in Neutrino Oscillation Experiments

Claudia Frugiuele, Marco G. Genoni, Michela Ignoti, Matteo G. A. Paris

hep-phhep-exquant-phSubmitted Feb 18, 2026• Announced Feb 19, 2026• 0 citations

arXiv HTML PDF

Abstract

θ_{13}

θ_{23}

, and

θ_{12}

, demonstrating their information-theoretic optimality for these parameters. In contrast, they are far from optimal for

δ_{CP}

. In particular, only a small fraction of the available information on

δ_{CP}

is extracted at the first maximum; the sensitivity improves at the second maximum, in line with the strategy of ESS

ν

SB, a planned facility. Second, the QFI associated with

δ_{CP}

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

δ_{CP}

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.

Journal reference: Journal of High Energy Physics 2026, 218 (2026)
DOI: 10.1007/JHEP08(2026)218
Comments: 21 pages, 11 figures

Related papers

Is the large uncertainty of $δ_{CP}$ fundamentally encoded in the neutrino quantum state?Is the large uncertainty of $δ_{CP}$ fundamentally encoded in the neutrino quantum state?

Michela Ignoti, Claudia Frugiuele, Matteo G. A. Paris +1 more

The precise measurement of the leptonic CP-violating phase $δ_{CP}$ remains one of the major open challenges in neutrino physics, as current experiments achieve only very limited accuracy. We address this issue through the lens of quantum estimation theory. A distinctive feature of neutrino oscillation experiments is that they cannot freely optimize the probe or measurement, since both are constrained by the production and detection of flavor eigenstates. We therefore examine whether the large uncertainty in $δ_{CP}$ originates from intrinsic reasons, either of the neutrino quantum state or of flavor measurements, or if it instead stems from experimental limitations. By comparing quantum and classical Fisher information, we demonstrate that the limited sensitivity to $δ_{CP}$ originates primarily from the information content of flavor measurements. Furthermore, we show that targeting the second oscillation maximum, as in the ESS $ν$ SB proposal, substantially enhances $δ_{CP}$ information compared to experiments centered on the first maximum.The precise measurement of the leptonic CP-violating phase $δ_{CP}$ remains one of the major open challenges in neutrino physics, as current experiments achieve only very limited accuracy. We address this issue through the lens of quantum estimation theory. A distinctive feature of neutrino oscillation experiments is that they cannot freely optimize the probe or measurement, since both are constrained by the production and detection of flavor eigenstates. We therefore examine whether the large uncertainty in $δ_{CP}$ originates from intrinsic reasons, either of the neutrino quantum state or of flavor measurements, or if it instead stems from experimental limitations. By comparing quantum and classical Fisher information, we demonstrate that the limited sensitivity to $δ_{CP}$ originates primarily from the information content of flavor measurements. Furthermore, we show that targeting the second oscillation maximum, as in the ESS$ν$SB proposal, substantially enhances $δ_{CP}$ information compared to experiments centered on the first maximum.

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hep-phCross-listedarXiv:2605.30404May 29, 20260 citations

Quantum estimation in neutrino oscillations

Edson C. M. Nogueira, de Souza, Gustavo, Adalberto D. Varizi +1 more

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.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.

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Quantum Fisher Information Revealing Parameter Sensitivity in Long-Baseline Neutrino Experiments

Bhavna Yadav, Amir Subba, Yu Shi

Determination of the leptonic CP-violating phase $δ_{\rm CP}$ , the atmospheric mixing angle $θ_{23}$ , and the mass-squared difference $Δm_{31}^2$ 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, $δ_{\rm CP}$ and $θ_{23}$ exhibit bimodal QFI profiles with peaks around $L/E \sim 500$ and $1500~\mathrm{km/GeV}$ , reaching $F_Q(δ_{\rm CP}) \sim 0.15$ and $F_Q(θ_{23}) \sim 15$ , respectively. In contrast, $F_Q(Δm_{31}^2)$ increases rapidly with $L/E$ over the range considered, reaching values of order $10^7$ . This hierarchy indicates that, within the considered single-parameter framework, the neutrino state carries substantially greater intrinsic quantum sensitivity to $Δm_{31}^2$ than to $θ_{23}$ or $δ_{\rm CP}$ . 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 $δ_{\rm CP}$ in the few-GeV region, while producing only minor modifications for $θ_{23}$ and $Δm_{31}^2$ . 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.Determination of the leptonic CP-violating phase $δ_{\rm CP}$, the atmospheric mixing angle $θ_{23}$, and the mass-squared difference $Δm_{31}^2$ 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, $δ_{\rm CP}$ and $θ_{23}$ exhibit bimodal QFI profiles with peaks around $L/E \sim 500$ and $1500~\mathrm{km/GeV}$, reaching $F_Q(δ_{\rm CP}) \sim 0.15$ and $F_Q(θ_{23}) \sim 15$, respectively. In contrast, $F_Q(Δm_{31}^2)$ increases rapidly with $L/E$ over the range considered, reaching values of order $10^7$. This hierarchy indicates that, within the considered single-parameter framework, the neutrino state carries substantially greater intrinsic quantum sensitivity to $Δm_{31}^2$ than to $θ_{23}$ or $δ_{\rm CP}$. 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 $δ_{\rm CP}$ in the few-GeV region, while producing only minor modifications for $θ_{23}$ and $Δm_{31}^2$. 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.

hep-phCross-listedarXiv:2602.05221Feb 6, 20260 citations

Multiparameter Quantum Estimation and Degeneracy Structure in Three-Flavor Neutrino Oscillations

Bhavna Yadav, Amir Subba, Yu Shi

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 $θ_{23}$ , $δ_{\mathrm{CP}}$ , 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 $(θ_{23},δ_{\mathrm{CP}})$ parameter space. Although different parameter sets can produce identical $ν_μ\rightarrowν_e$ 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.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 $θ_{23}$, $δ_{\mathrm{CP}}$, 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 $(θ_{23},δ_{\mathrm{CP}})$ parameter space. Although different parameter sets can produce identical $ν_μ\rightarrowν_e$ 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.

hep-phCross-listedarXiv:2606.30222Jun 30, 20260 citations

θ_{13}

θ_{23}

, and

θ_{12}

, demonstrating their information-theoretic optimality for these parameters. In contrast, they are far from optimal for

δ_{CP}

. In particular, only a small fraction of the available information on

δ_{CP}

is extracted at the first maximum; the sensitivity improves at the second maximum, in line with the strategy of ESS

ν

SB, a planned facility. Second, the QFI associated with

δ_{CP}

δ_{CP}

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.

Is the large uncertainty of

δ_{CP}

fundamentally encoded in the neutrino quantum state?

The precise measurement of the leptonic CP-violating phase

δ_{CP}

remains one of the major open challenges in neutrino physics, as current experiments achieve only very limited accuracy. We address this issue through the lens of quantum estimation theory. A distinctive feature of neutrino oscillation experiments is that they cannot freely optimize the probe or measurement, since both are constrained by the production and detection of flavor eigenstates. We therefore examine whether the large uncertainty in

δ_{CP}

originates from intrinsic reasons, either of the neutrino quantum state or of flavor measurements, or if it instead stems from experimental limitations. By comparing quantum and classical Fisher information, we demonstrate that the limited sensitivity to

δ_{CP}

originates primarily from the information content of flavor measurements. Furthermore, we show that targeting the second oscillation maximum, as in the ESS

ν

SB proposal, substantially enhances

δ_{CP}

information compared to experiments centered on the first maximum.

Leptonic CP Phase Determination from Fisher Information in NO

ν

A and T2K

The precise determination of the leptonic CP phase

δ_{\rm CP}

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

δ_{\rm CP}

is intrinsically encoded in neutrino states and how efficiently it is extracted in present LBL experiments such as T2K and NO

ν

A. 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

δ_{\rm CP}

. Our analysis provides a complementary information-theoretic perspective on precise estimation of oscillation parameters in LBL neutrino experiments.

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.

Determination of the leptonic CP-violating phase

δ_{\rm CP}

, the atmospheric mixing angle

θ_{23}

, and the mass-squared difference

Δm_{31}^2

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,

δ_{\rm CP}

and

θ_{23}

exhibit bimodal QFI profiles with peaks around

L/E \sim 500

and

1500~\mathrm{km/GeV}

, reaching

F_Q(δ_{\rm CP}) \sim 0.15

and

F_Q(θ_{23}) \sim 15

, respectively. In contrast,

F_Q(Δm_{31}^2)

increases rapidly with

L/E

over the range considered, reaching values of order

10^7

. This hierarchy indicates that, within the considered single-parameter framework, the neutrino state carries substantially greater intrinsic quantum sensitivity to

Δm_{31}^2

than to

θ_{23}

δ_{\rm CP}

. 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

δ_{\rm CP}

in the few-GeV region, while producing only minor modifications for

θ_{23}

and

Δm_{31}^2

. 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.

θ_{23}

δ_{\mathrm{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_{\mathrm{CP}})

parameter space. Although different parameter sets can produce identical

ν_μ\rightarrowν_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.