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Effect of Off-diagonal NSI Parameters on Entanglement Measurements in Neutrino Oscillations

T0 review · 1 major / 2 minor · reviewed 2026-05-19 · grok-4.3

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Pith's one-line read Off-diagonal NSI parameters alter neutrino entanglement measures most at low energies, with Negativity most sensitive to the CP phase.

desk verdict This paper maps off-diagonal NSI onto neutrino entanglement measures for DUNE but the probability-only formulas likely miss relative phase effects from the full evolution operator. read the letter →

arxiv 2507.04885 v2 submitted 2025-07-07 hep-ph

Lekhashri Konwar , Papia Panda , Rukmani Mohanta This is my paper · ORCID
classification hep-ph
keywords neutrinooscillationsnon-standardinteractionsquantumentanglementDUNEexperimentCPviolationoff-diagonalNSI
checked against Cost.FunctionalEquation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper explores how off-diagonal non-standard interaction parameters influence quantum entanglement in three-flavor neutrino oscillations. It rewrites the measures of entanglement of formation, concurrence, and negativity as functions of oscillation probabilities and tracks their changes under the parameters ε_eμ, ε_eτ, and ε_μτ for a DUNE-like setup. The results indicate that NSI effects stand out most clearly at lower energies, that negativity remains the strongest measure even as energy rises, and that it alone displays a pronounced dependence on the CP-violating phase in the energy plane. Different NSI parameters act through appearance or disappearance channels. A reader would care because the work supplies a quantum-information route to testing beyond-standard-model effects in neutrino data.

What carries the argument

The rewriting of entanglement measures (EOF, concurrence, negativity) as functions of neutrino oscillation probabilities, followed by their evaluation under off-diagonal NSI parameters.

What would settle it

A DUNE measurement showing that the entanglement measures lack stronger NSI dependence at low energies or that negativity fails to remain dominant at high energies would falsify the central claim.

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Extended reading notes

Core claim

Expressing entanglement of formation, concurrence, and negativity directly in terms of oscillation probabilities shows that the off-diagonal NSI parameters ε_eμ, ε_eτ, and ε_μτ, together with their phases, modify these quantum correlations, with the largest changes appearing at low energies in DUNE while negativity continues to dominate at higher energies and exhibits clearer sensitivity to δ_CP than the other two measures.

Load-bearing premise

The entanglement measures can be extracted solely from oscillation probabilities without additional experimental or theoretical corrections that would alter the reported NSI dependence.

Editorial extensions

If this is right

  • NSI effects would be most detectable in the low-energy region of long-baseline neutrino data.
  • Negativity would continue to register quantum correlations after EOF and concurrence weaken at high energies.
  • ε_eμ and ε_eτ would mainly modify entanglement through appearance-channel probabilities, while ε_μτ would act through disappearance channels.
  • Negativity would display a visible dependence on δ_CP within specific low-energy intervals under off-diagonal NSI.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same probability-based mapping could be applied to other long-baseline experiments to search for consistent NSI signatures.
  • Entanglement observables might supplement conventional oscillation fits when placing bounds on NSI parameters.
  • Low-energy runs could be prioritized to separate NSI contributions from standard oscillations using these measures.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 2 minor

Summary. The paper explores the effects of off-diagonal NSI parameters (ε_eμ, ε_eτ, ε_μτ and their phases) on quantum entanglement in three-flavor neutrino oscillations. It expresses Entanglement of Formation (EOF), Concurrence, and Negativity in terms of oscillation probabilities, analyzes their behavior with DUNE as reference, and reports that NSI effects are strongest at low energies, Negativity dominates at higher energies, ε_eμ and ε_eτ primarily affect the appearance channel while ε_μτ affects disappearance, and Negativity shows greater sensitivity to δ_CP in the [E – δ_CP] plane under off-diagonal NSI.

Significance. If the expressions for the entanglement measures are shown to correctly incorporate all relevant phase information from the evolution operator, the work could provide a quantum-information-based approach to probing NSI in long-baseline experiments, with the reported differential sensitivities offering potential guidance for analysis strategies at DUNE and similar facilities.

major comments (1)
  1. [Section on quantum correlation measures] Section on quantum correlation measures (abstract and the section deriving entanglement measures from probabilities): The entanglement measures are expressed solely as functions of the oscillation probabilities P_αβ. For the pure state |ψ⟩ = ∑_β A_β |ν_β⟩ the density matrix has off-diagonal coherences √(P_α P_β) exp(i Δϕ_αβ), where the relative phases Δϕ_αβ are fixed by the full evolution operator containing both δ_CP and the complex phases of ε_eμ, ε_eτ, ε_μτ. Formulas discarding explicit phase information therefore cannot capture the full dependence on δ_CP and NSI phases reported in the [E – δ_CP] plane, especially at low energies where matter and NSI effects are stated to be largest. This is load-bearing for the central sensitivity claims.
minor comments (2)
  1. [Abstract and methods] The abstract and methods sections provide no error propagation for the entanglement measures derived from probabilities and no explicit baseline comparison to the standard oscillation case without NSI.
  2. [Numerical results] The numerical results lack a clear statement of how the NSI parameter magnitudes and phases are chosen or marginalized, which affects reproducibility of the reported [E – δ_CP] sensitivities.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for identifying an important technical point regarding the treatment of phases in the entanglement measures. We address this comment below and will revise the manuscript to strengthen the presentation and accuracy of our results.

read point-by-point responses

  1. Referee: Section on quantum correlation measures (abstract and the section deriving entanglement measures from probabilities): The entanglement measures are expressed solely as functions of the oscillation probabilities P_αβ. For the pure state |ψ⟩ = ∑_β A_β |ν_β⟩ the density matrix has off-diagonal coherences √(P_α P_β) exp(i Δϕ_αβ), where the relative phases Δϕ_αβ are fixed by the full evolution operator containing both δ_CP and the complex phases of ε_eμ, ε_eτ, ε_μτ. Formulas discarding explicit phase information therefore cannot capture the full dependence on δ_CP and NSI phases reported in the [E – δ_CP] plane, especially at low energies where matter and NSI effects are stated to be largest. This is load-bearing for the central sensitivity claims.

    Authors: We thank the referee for this insightful comment. We agree that the off-diagonal elements of the density matrix for the pure neutrino state contain relative phases Δϕ_αβ that are determined by the full evolution operator and therefore depend on both δ_CP and the complex NSI phases. Our analytic expressions for EOF, Concurrence, and Negativity were written in a form that depends only on the probabilities P_αβ; this presentation omits explicit phase dependence and is therefore incomplete for capturing the full sensitivity structure. In the numerical DUNE analysis we did evolve the complete Hamiltonian (including all phases) to obtain the state amplitudes before computing the measures, but the manuscript does not make this distinction clear and the formulas as written do not retain the phases. We will revise the relevant section to express the measures directly from the full density-matrix elements ρ_αβ = A_α A_β^*, thereby incorporating both probabilities and phases. The abstract will also be updated to reflect the corrected derivation. These changes will ensure that the reported δ_CP and NSI-phase sensitivities in the [E – δ_CP] plane are rigorously justified. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; derivation substitutes NSI probabilities into independent entanglement formulas

full rationale

The paper computes oscillation probabilities modified by off-diagonal NSI parameters (including phases) using the standard three-flavor evolution Hamiltonian, then inserts those probabilities into the standard expressions for EOF, concurrence, and negativity. No step reduces by construction to a fitted parameter, self-defined quantity, or self-citation chain. The entanglement formulas are taken from external quantum-information literature and applied directly; DUNE baseline and energy ranges are external inputs, not derived inside the work. The chain is therefore self-contained against external benchmarks and does not exhibit any of the enumerated circularity patterns.

Assumptions & free parameters 1 free parameters · 1 assumptions · 0 invented entities

The analysis rests on the standard three-flavor oscillation Hamiltonian plus the usual NSI parameterization; no new particles or forces are introduced. The only free parameters are the three off-diagonal NSI magnitudes and phases, which are scanned rather than fitted to new data.

free parameters (1)
  • ε_eμ, ε_eτ, ε_μτ magnitudes and phases
    Scanned over representative ranges to illustrate effects; values are not derived from first principles or external data within the paper.
assumptions (1)
  • domain assumption Three-flavor neutrino oscillation framework with standard matter effects remains valid when off-diagonal NSI are added
    Invoked throughout the probability calculations and entanglement mappings.

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Cite this review

Pith. "Pith review of Effect of Off-diagonal NSI Parameters on Entanglement Measurements in Neutrino Oscillations." pith.science (2026). https://pith.science/paper/2507.04885

@misc{pith2026250704885,
  author       = {Pith},
  title        = {Pith review of: Effect of Off-diagonal NSI Parameters on Entanglement Measurements in Neutrino Oscillations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2507.04885}},
  note         = {Machine review of arXiv:2507.04885}
}
abstract

In this work, we explore the influence of off-diagonal non-standard interaction (NSI) parameters on quantum entanglement within the three-flavor neutrino oscillation framework. By expressing three key entanglement measures: Entanglement of Formation (EOF), Concurrence, and Negativity in terms of oscillation probabilities, we analyze how these quantum correlations are affected by the NSI parameters $\epsilon_{e\mu}$, $\epsilon_{e\tau}$, and $\epsilon_{\mu\tau}$, including their complex phases. The quantum correlation measures considered in this work cannot be extracted directly from event rates, but solely in terms of oscillation probabilities. Using the DUNE experiment as a reference point, our analysis shows that NSI effects are most pronounced at lower energies, while Negativity continuing to dominate even at higher energies. It is observed that $\epsilon_{e \mu}$ and $\epsilon_{e \tau}$ affect entanglement measures mainly through the appearance channel, while the impact of $\epsilon_{\mu \tau}$ on EOF, Concurrence, and Negativity is predominantly linked to the disappearance channel. Further, our results show that Negativity is more sensitive than EOF and Concurrence in the [Energy ($E$) - $\delta_{CP}$] plane under the influence of off-diagonal NSI scenarios, displaying a clear dependence of the CP-violating phase, $\delta_{CP}$ on specific energy ranges, particularly in the lower energy regime.

Figures

Figures reproduced from arXiv: 2507.04885 by the authors.

Figure 1
Figure 1. FIG. 1: Upper (lower) row shows the appearance probability as a function of neutrino [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Upper (lower) row shows the effect of each term containing [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Upper (lower) row shows the effect of each term containing [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4: The disappearance probability as a function of neutrino energy for the DUNE [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: The effect of each term containing [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Upper (lower) row shows the NSI parameter ( [PITH_FULL_IMAGE:figures/full_fig_p019_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Upper (lower) row shows the NSI parameter ( [PITH_FULL_IMAGE:figures/full_fig_p020_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Upper (lower) row shows the NSI parameter ( [PITH_FULL_IMAGE:figures/full_fig_p021_8.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quantum Information as a New Lens for Precision Neutrino Physics

    hep-ph 2026-06 unverdicted novelty 6.0 of 10

    Concurrence minima in neutrino oscillations identify low-entanglement energy regions that, when aligned with NOνA and T2K data, yield tighter joint constraints on sin²θ₂₃, δ_CP, and Δm²₃₁.

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