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arxiv: 2605.30404 · v1 · pith:4SVEIE2Rnew · submitted 2026-05-28 · ✦ hep-ph · quant-ph

Leptonic CP Phase Determination from Fisher Information in NOνA and T2K

Neetu Raj Singh Chundawat , Luis A. Delgadillo , Yu-Feng Li This is my paper

Pith reviewed 2026-06-29 06:24 UTC · model grok-4.3

classification ✦ hep-ph quant-ph
keywords neutrino oscillationsCP violationFisher informationquantum estimationT2KNOvAlong-baseline neutrinosleptonic CP phase
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The pith

T2K and NOνA extract only a small fraction of the quantum information about the leptonic CP phase δ_CP.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies quantum estimation theory to long-baseline neutrino experiments. It first computes the quantum Fisher information that neutrino and antineutrino states carry about δ_CP, showing how matter effects shape this information according to mass ordering. It then calculates the classical Fisher information obtainable from the reconstructed event spectra of T2K and NOνA under Poisson statistics. The comparison shows that both experiments recover only a modest portion of the intrinsic quantum information, and that this recovery drops sharply near values of δ_CP that produce maximal CP violation because the observed spectra become less sensitive to small phase changes. This information gap directly limits how precisely the phase can be determined with present data sets.

Core claim

The authors show that the quantum states of neutrinos encode a finite amount of information about δ_CP whose structure depends on matter effects and the mass ordering. When this intrinsic content is compared with the event-level Fisher information extracted from the actual reconstructed spectra in T2K and NOνA, the experiments are found to access only a small fraction of the available information, with the shortfall most pronounced near maximally CP-violating values of the phase where spectral variations with δ_CP are reduced.

What carries the argument

Quantum Fisher information of the neutrino state with respect to δ_CP, set against the classical Fisher information obtained from binned event rates under Poisson statistics.

If this is right

  • The ultimate precision on δ_CP remains bounded by the fraction of quantum information that can be extracted from flavor-tagged event counts.
  • Near maximal CP violation the reconstructed spectra lose sensitivity, directly reducing the ability to resolve small changes in the phase.
  • Matter effects produce distinct information patterns for normal and inverted mass orderings, affecting how much information each experiment can access.
  • Even the combined T2K plus NOνA data set still leaves most of the quantum information about δ_CP unused.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Measurements that go beyond standard flavor identification, such as more complete reconstruction of the final-state kinematics, could in principle recover a larger share of the quantum information.
  • The same comparison between quantum and event-level Fisher information could be applied to proposed future experiments to identify design choices that raise extraction efficiency.
  • The reduced sensitivity near maximal CP violation suggests that statistical power alone does not explain the full experimental difficulty; the shape of the likelihood surface itself is the limiting factor.
  • If the gap between quantum and classical information persists across different analysis methods, it would indicate that new observable channels, rather than larger statistics, are needed to improve constraints on δ_CP.

Load-bearing premise

That the Poisson likelihood constructed from reconstructed energy and flavor spectra fully represents all experimentally accessible information about δ_CP.

What would settle it

A re-analysis of T2K or NOνA data near δ_CP = ±π/2 that finds the event distributions vary more rapidly with small phase shifts than the computed event-level Fisher information predicts.

Figures

Figures reproduced from arXiv: 2605.30404 by Luis A. Delgadillo, Neetu Raj Singh Chundawat, Yu-Feng Li.

Figure 1
Figure 1. Figure 1: FIG. 1. QFI associated with [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The probability asymmetry [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Expected [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Expected [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Event-weighted QFI [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Event-weighted QFI [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: presents the event-level Fisher information distributions for the T2K configuration. The dominant information region (Fevent(Eν, δCP) ∼ 0.2) appears near the first oscillation maximum around Eν ∼ 0.6 GeV and close to the CP-conserving phases δCP = 0 and ±π. Due to the shorter baseline and consequently weaker matter effects, the neutrino and antineutrino modes exhibit comparatively similar overall structure… view at source ↗
Figure 8
Figure 8. Figure 8: shows the corresponding event-level Fisher information distributions for the NOνA configuration. For both orderings, the neutrino mode exhibits the dominant information region (Fevent(Eν, δCP) ∼ 1.2) near the first oscillation maximum around Eν ∼ 2 GeV, par￾ticularly close to the CP-conserving phases δCP = 0 and ±π, while the antineutrino mode carries comparatively smaller information. Unlike the T2K confi… view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Extraction efficiency [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Total extraction efficiency [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
read the original abstract

The precise determination of the leptonic CP phase $\delta_{\rm CP}$ 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 $\delta_{\rm CP}$ is intrinsically encoded in neutrino states and how efficiently it is extracted in present LBL experiments such as T2K and NO$\nu$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 $\delta_{\rm CP}$. Our analysis provides a complementary information-theoretic perspective on precise estimation of oscillation parameters in LBL neutrino experiments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript applies quantum estimation theory to long-baseline neutrino experiments, computing the quantum Fisher information (QFI) for the CP phase δ_CP encoded in neutrino and antineutrino states (including matter effects) and comparing it to the classical Fisher information extracted from binned event spectra via Poisson statistics in T2K and NOνA. The central claim is that both experiments capture only a small fraction of the intrinsic information, with extraction efficiency particularly suppressed near maximal CP violation.

Significance. If the numerical results hold, the work supplies a concrete information-theoretic benchmark for the efficiency of flavor measurements in current LBL experiments. It quantifies the gap between the quantum limit and the practically accessible information under the standard POVM, and the mass-ordering dependence arising from matter effects is a useful addition. The approach is standard for quantum-vs-classical estimation comparisons and could inform detector or analysis upgrades.

major comments (2)
  1. [Abstract] The abstract states that experiments 'extract only a small fraction' and that efficiency is 'particularly suppressed' near maximal CP violation, but supplies no numerical values, error estimates, or validation against known limits (e.g., the δ_CP-independent case or the vacuum limit). Without these in the main text or figures, the magnitude of the claimed suppression cannot be assessed.
  2. The comparison assumes that the Poisson-based event Fisher information on reconstructed spectra fully represents the experimentally accessible information. While this is the correct benchmark for the chosen measurement, the manuscript should explicitly state the binning, energy resolution, and efficiency assumptions used to compute the classical FI, as these directly affect the reported extraction efficiency.
minor comments (2)
  1. Notation for the quantum state propagation (including matter Hamiltonian) and the explicit form of the QFI matrix element for δ_CP should be given in an early section to allow readers to reproduce the mass-ordering dependence.
  2. [Abstract] The abstract would be strengthened by a single quantitative statement (e.g., 'extraction efficiency drops to X% near δ_CP = 3π/2') even if the detailed plots appear later.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and positive assessment of the significance of our work. We address each major comment below and have revised the manuscript to improve clarity and completeness.

read point-by-point responses

  1. Referee: [Abstract] The abstract states that experiments 'extract only a small fraction' and that efficiency is 'particularly suppressed' near maximal CP violation, but supplies no numerical values, error estimates, or validation against known limits (e.g., the δ_CP-independent case or the vacuum limit). Without these in the main text or figures, the magnitude of the claimed suppression cannot be assessed.

    Authors: The main text and figures already contain the detailed numerical comparisons of quantum and classical Fisher information, including the δ_CP dependence and matter-effect-induced mass-ordering structure, with explicit results for both T2K and NOνA. However, we agree that the abstract would benefit from summarizing key quantitative benchmarks to allow immediate assessment of the claimed suppression. In the revised manuscript we have updated the abstract to include approximate extraction efficiencies drawn from our calculations and a brief reference to the vacuum-limit validation (where the two Fisher informations coincide in the absence of matter effects). revision: yes

  2. Referee: The comparison assumes that the Poisson-based event Fisher information on reconstructed spectra fully represents the experimentally accessible information. While this is the correct benchmark for the chosen measurement, the manuscript should explicitly state the binning, energy resolution, and efficiency assumptions used to compute the classical FI, as these directly affect the reported extraction efficiency.

    Authors: We agree that the assumptions entering the classical Fisher information must be stated explicitly. The original manuscript references the standard T2K and NOνA configurations, but we have now added a dedicated paragraph (in the section describing the classical FI calculation) that specifies the energy binning, energy-resolution smearing model, and detection-efficiency parametrizations employed. This addition ensures full reproducibility and clarifies the precise scope of the reported extraction efficiencies. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The derivation computes the quantum Fisher information directly from the neutrino state evolution (including matter effects) and the classical event-level Fisher information from Poisson statistics on reconstructed flavor spectra. These are independent quantities by construction: QFI bounds the precision over any measurement while the Poisson FI is the information for the specific flavor POVM used in the experiments. No equation reduces a claimed result to a fitted parameter, self-citation chain, or input by definition. The comparison of extraction efficiency is a standard quantum-vs-classical estimation exercise and remains self-contained without load-bearing self-citations or ansatz smuggling.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract, no explicit free parameters, axioms, or invented entities are introduced; the work relies on standard quantum Fisher information and Poisson statistics.

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discussion (0)

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Forward citations

Cited by 1 Pith paper

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