Steering in Neutrino Oscillations with Non-Standard Interaction

Bhavna Yadav; Lekhashri Konwar

REVIEW 3 major objections 3 minor 65 references

Steering in Neutrino Oscillations with Non-Standard Interaction

T0 review · 3 major / 3 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper argues that quantum steering in neutrino oscillations is measurably altered by non-standard interactions, with DUNE showing a 21% deviation from the Standard Model at its peak-flux energies.

desk verdict The paper's central 'steering' numbers are driven by a trace criterion that is not equivalent to any standard steering inequality; the oscillation-probability algebra is clean, but the main interpretation is unsupported. read the letter →

arxiv 2411.14234 v2 pith:AQBKXQZK submitted 2024-11-21 hep-ph

Lekhashri Konwar , Bhavna Yadav This is my paper · ORCID

classification hep-ph

keywords quantumsteeringneutrinooscillationsnon-standardinteractionDUNENOvAthree-flavormixingBellnonlocalityconcurrence

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 argues that quantum steering—the ability of one neutrino's flavor measurement to change what can be predicted about a partner neutrino's state—is a practical probe of new physics in neutrino oscillations. The authors show that the maximum steering value of a three-flavor neutrino state, $S_{\max}$, is a simple function of the three oscillation probabilities $P_{\alpha e}, P_{\alpha \mu}, P_{\alpha \tau}$, so it can be computed directly from measured oscillation data. Applying this to the NOvA and DUNE experiment geometries with a Standard Model plus non-standard interaction (NSI) Hamiltonian, they find that DUNE's longer baseline makes steering noticeably more NSI-sensitive: around DUNE's peak-flux energies, $S_{\max}$ deviates by about 21% from the Standard Model prediction for normal mass ordering and rises about 15% for inverted ordering. If correct, this gives a new, oscillation-probability-based route to spotting NSI effects and to comparing entanglement, steering, and Bell nonlocality in the same neutrino system.

What carries the argument

The load-bearing object is quantum steering—Alice's ability to update Bob's state by a local measurement—quantified by the steering measure $S_{AB} = \mathrm{Tr}(T_{AB}^{T} T_{AB})$ built from the correlation matrix $T_{AB}$ of a two-qubit reduced state. For a three-flavor neutrino in the flavor-mode encoding $|\nu_e\rangle = |100\rangle$, $|\nu_\mu\rangle = |010\rangle$, $|\nu_\tau\rangle = |001\rangle$, the three bipartite reduced states yield $S_{AB}$, $S_{AC}$, $S_{BC}$, and their maximum $S_{\max} = \max\{S_{AB}, S_{AC}, S_{BC}\}$. The key identity is that each $S$ collapses to a polynomial in the oscillation probabilities, for example $S_{AB} = 8P_{\alpha e}P_{\alpha \mu} + [P_{\alpha \tau} - P_{\alpha e} - P_{\alpha \mu}]^2$, so the whole steering analysis reduces to computing those probabilities. The probabilities themselves come from the evolution operator $U_f(L)$ of the three-flavor Hamiltonian with matter potential plus NSI parameters $\epsilon_{\alpha\beta}$, and the experimental numbers use the NOvA and DUNE baselines and flux ranges. This machinery lets the authors translate any modification of oscillation probabilities—including NSI-induced ones—directly into a modification of the steering witness.

What would settle it

Compute the same DUNE curves using the general two-setting steering parameter—the sum of the two largest singular values of each correlation matrix—in place of $\mathrm{Tr}(T^T T)$; if the $S_{\max} > 1$ windows or the reported 21% and 15% NSI deviations shift materially, the paper's central numerical claim fails.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is a set of closed-form expressions—Eqs. (42)–(45)—that write the steering measures $S_{AB}$, $S_{AC}$, $S_{BC}$, and their maximum $S_{\max}$ entirely in terms of three-flavor neutrino oscillation probabilities; this formula is valid for vacuum oscillations and, because it uses probabilities, also for NSI-modified oscillations. From those expressions, the paper numerically finds that in the DUNE setup, within the energy window $[2.3, 3.1]$ GeV where DUNE's flux peaks, including NSI changes $S_{\max}$ by about 21% below the Standard Model value for normal ordering and by about 15% above it for inverted ordering. The same comparison for NOvA produces smaller or energy-dependent shifts. Throughout the studied energies $S_{\max}$ stays above 1, which the paper interprets as the neutrino states being steerable, and the DUNE comparison of Bell-CHSH, steering, and concurrence exhibits the expected hierarchy: Bell nonlocality implies steering implies entanglement, but not conversely. The paper also derives exact relations between the pairwise steering measures and the pairwise concurrences of the three-qubit flavor state.

Load-bearing premise

The results assume that the simple correlation-matrix condition 'trace of $T^T T$ exceeds 1' exactly matches the accepted definition of two-setting steerability for the neutrino states considered; if it only approximates it, the regions labeled steerable, and the 21% and 15% deviation numbers, could change.

Editorial extensions

If this is right

Because $S_{\max}$ is a function only of $P_{\alpha e}$, $P_{\alpha \mu}$, and $P_{\alpha \tau}$ (Eq. (45)), any experiment that measures three-flavor oscillation probabilities can compute the steering witness directly, without additional quantum measurements.
In DUNE's peak-flux window $[2.3, 3.1]$ GeV, NSI shifts $S_{\max}$ by about 21% for normal ordering and about 15% for inverted ordering, making steering a more sensitive NSI indicator there than the shorter-baseline NOvA.
When $P_{\alpha \tau} = 0$, the three-flavor formula reduces to the two-flavor result $S_{AB} = (P_{\alpha e} + P_{\alpha \mu})^2 + 8P_{\alpha e}P_{\alpha \mu}$, linking the new expressions to the existing two-flavor literature.
The relations $S_{AB} = 1 + 2C_{AB}^2 - C_{AC}^2 - C_{BC}^2$ (and cyclic versions) tie steering violations directly to pairwise concurrences, so pairwise entanglement measurements bound the steering inequality.
The DUNE comparison of Bell-CHSH, steering, and concurrence shows the expected nesting of nonlocality, steering, and entanglement, with steering present at all energies studied and the hierarchy respected.

Reading between the lines

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

Beyond the paper's explicit claims: the probability-only form of $S_{\max}$ means DUNE could report an $S_{\max}$-versus-energy curve from reconstructed oscillation probabilities, and persistence of the 21%/15% NSI deviations in such a curve would be a new, largely systematic-independent NSI diagnostic.
The trace criterion $\mathrm{Tr}(T^T T) > 1$ is not the general two-setting steering parameter; checking whether the general sum-of-two-largest-singular-values condition changes the steerable regions would settle whether the reported windows and percentages are artifacts of the adopted criterion.
The same probability-polynomial construction applies to any three-flavor unitary evolution, so with appropriate probabilities it could also probe sterile mixing, non-unitarity, or modified matter potentials in the same steering language.
The concurrence relations suggest a possible entanglement-based lower bound on steering in mixed flavor states; whether the pure-state formulas survive partial tracing in realistic detector scenarios is a direct testable extension.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

You should know this before reading: the headline 21%/15% numbers are about a quantity that is probably not quantum steering. Eq. (19) asserts the iff criterion S_AB = Tr(T^T T) > 1 for two-setting steerability, citing [35]. The two-setting linear steering inequality of Cavalcanti et al. is violated when the sum of the two largest singular values of T exceeds sqrt(2), not when the Frobenius norm squared exceeds 1. The stress-test note gives a concrete counterexample from the paper's own state family: with P_tau=0.30, P_mu=P_e=0.35, S_AB=1.14>1 while the maximized two-setting expression is (s1+s2)/sqrt(2)=0.99<1. So the trace condition is at best a sufficient witness, not an iff, and the claim that Smax>1 means steerable does not follow. Unless [35] proved a special equivalence for this rank-deficient class—which the paper does not demonstrate—the word 'steering' in the abstract and conclusions is doing work it cannot support.

What is actually new and useful: the paper gives a clean three-flavor expression for the trace measure in terms of oscillation probabilities (Eqs. 42-45), checks the two-flavor limit, and connects it to concurrence. That algebra is correct. The numerical study of how NSI shifts this trace measure in NOvA and DUNE is a legitimate scenario exercise, even if the name 'steering' is wrong.

The other soft spots are real but minor by comparison. The NSI plots use a single point inside the 2-sigma ranges of Table II, with no error bands, so the 21%/15% numbers cannot be independently reproduced. There is also a text-figure mismatch for NOvA energy values that the figures do not resolve.

Bottom line: this is a salvageable paper, but the central interpretational claim is currently unsupported. The authors should either prove that their trace measure is equivalent to a genuine steering inequality for this state class, or recompute with the standard two-setting measure—and then the 21% claim may change. As it stands, a careful reader cannot trust the 'steering' part. Worth sending to referees, because the issue is subtle and fixable, but I would not cite it in its current form.

Referee Report

3 major / 3 minor

Summary. The paper studies quantum steering in three-flavor neutrino oscillations in the presence of non-standard interactions (NSI). It derives formulas for the quantity S_max, defined as the maximum of Tr(T^T T) over the three reduced two-qubit states of a single-excitation three-flavor state, and expresses S_max directly in terms of oscillation probabilities (Eqs. 42-45). Using standard oscillation parameters and NSI ranges from external fits, it computes S_max for NOvA and DUNE under both mass orderings and reports characteristic deviations of the NSI case from the Standard Model, notably about 21% for DUNE normal ordering and about 15% for inverted ordering in the multi-GeV energy range. The paper also compares steering with Bell-CHSH nonlocality and concurrence, and gives relations between S_AB and reduced concurrences.

Significance. If the steering interpretation were valid, the paper would provide an interesting bridge between neutrino oscillation phenomenology and quantum information: explicit probability-only formulas for a correlation quantifier, a concrete comparison of nonlocality, steering, and entanglement in long-baseline experiments, and a falsifiable prediction that NSI shifts the quantifier by tens of percent in DUNE. The analytical content is explicit and checkable, and the setup uses externally fitted oscillation and NSI parameters rather than fitting to the target result, so there is no obvious circularity. However, the central physical claim hinges on the steering criterion in Eq. (19), and that criterion is not supported by the paper's own stated framework. The numerical conclusions are also presented for a single, incompletely specified NSI benchmark, so the headline percentages are not independently reproducible as stated.

major comments (3)

[Section III, Eq. (19); Section IV, Eqs. (42)-(45); Section V] The criterion S_AB = Tr(T^T T) > 1 is asserted as an if-and-only-if condition for two-setting steering, citing Ref. [35], but it is inconsistent with the Cavalcanti inequality in Eq. (17). For n=2, the maximum of Eq. (17) is F_2 = (1/sqrt(2)) sqrt(lambda_1+lambda_2), where lambda_i are the eigenvalues of T^T T, so two-setting steerability requires lambda_1+lambda_2 > 2, not Tr(T^T T) > 1. For the reduced states in Eqs. (30)-(32), the correlation matrix has singular values s1=s2=2 sqrt(P_mu P_e) and s3=|P_tau - P_mu - P_e|, giving F_2 = 2 sqrt(P_mu P_e), which is at most 1 for all physical probabilities since P_mu+P_e <= 1. Thus no state of the single-excitation form studied in this paper ever violates the two-setting steering inequality. Concretely, taking P_tau=0.30, P_mu=P_e=0.35 gives S_AB=1.14 by Eq. (42), but F_2=0.7<1. Therefore the interpretation of S_max>1 as steering, and the derived 21% and 15% claims in the abstract and Section V, are unsupported without a proof that Ref. [35] establishes an equivalence for this specific class of states. The trace condition is at best a necessary condition for two-setting steerability, not a sufficient one.
[Section V and Table II] The numerical NSI curves are said to use the 2 sigma upper limits of Table II, but Table II lists ranges, several of which are unions of disjoint intervals, and the text does not specify which point in each range is used or whether all parameters are set simultaneously. The 21% and 15% deviation numbers therefore cannot be independently reproduced from the information given. Please state the exact benchmark values and show how the results vary across the allowed NSI ranges, for instance with uncertainty bands.
[Section V, paragraph on NOvA; Figure 1] The text states that in the SM the NOvA steering maximum occurs at E=0.8 GeV for NO and E=1.26 GeV for IO, but Figure 1 shows an energy axis from 2 to 10 GeV, so the cited energies are outside the plotted range. This mismatch makes the NOvA comparison, including the claimed enhancements at E approximately 1.26 GeV, unverifiable as presented. The figure or the text should be corrected so that the quantitative statements refer to the same energy range.

minor comments (3)

[Figure 1] The horizontal axis label reads "Energy(Gev)" and the axis appears duplicated in the extracted figure; please correct the typo and the layout.
[Table II] For parameters such as epsilon_ee and epsilon_mu_mu, the quoted 2 sigma ranges are unions of two disjoint intervals; the phrase "upper limit" should define whether the largest positive endpoint or the boundary of the full interval is used.
[Section IV, Eq. (45)] Equation (45) is stated to be valid for vacuum oscillations and for NSI-modified probabilities, but the derivation assumes a single-excitation three-qubit pure state; please state explicitly that NSI enters only through the replacement of the probabilities P_alpha beta by their NSI-modified values.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the NSI-induced steering shifts are computed from externally specified oscillation parameters and the steering-probability relation is derived from the density matrix, not assumed.

full rationale

The paper's central claim—that S_max changes by about 21% (NO) and 15% (IO) between SM and NSI at DUNE—is a numerical evaluation of a defined function S_max = max{S_AB, S_AC, S_BC} acting on externally fitted oscillation parameters (Tables I and II). The S_i expressions in Eqs. (39)–(44) are obtained by explicit trace computations on the reduced density matrices (30)–(32), and they reduce to the cited two-flavor result [51] in the P_tau=0 limit. No parameter appearing in the final figure is fitted to the target steering value, and no prediction is defined in terms of the answer it claims to predict. The paper does cite prior work by the same group ([30], [32], [33]) and by others, but only as background on quantum correlations in neutrino oscillations; none of these citations is invoked as the justification for the NSI shift or for the steering-probability formula. The only serious concern is physical correctness, not circularity: Eq. (19) imports an iff two-setting steering criterion from Ref. [35], whereas Cavalcanti-type inequalities involve singular values of T, and the paper does not prove equality for its X-shaped reduced states. A questionable imported criterion, or a claimed iff that may overstate a sufficient witness, is a benchmark/correctness issue; it is not a reduction of the paper's output to its own inputs.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central calculation depends mainly on external inputs: NSI parameters from a global fit, oscillation parameters from NuFit, and the mode-entanglement picture of neutrino flavor. The steering formulas are derived from these inputs, not from a new principle. No new particles or forces are introduced.

free parameters (6)

epsilon_ee = 2 sigma upper limit from [56], up to 1.4
Chosen at boundary of allowed region for the NSI plots.
epsilon_e_mu = 2 sigma upper limit from [56], up to 0.09
Chosen at boundary of allowed region.
epsilon_e_tau = 2 sigma upper limit from [56], up to 0.30
Chosen at boundary of allowed region.
epsilon_mu_mu = 2 sigma upper limit from [56], up to 1.4
Chosen at boundary of allowed region.
epsilon_mu_tau = 2 sigma upper limit from [56], up to 0.021
Chosen at boundary of allowed region.
epsilon_tau_tau = 2 sigma upper limit from [56], up to 1.4
Chosen at boundary of allowed region.

assumptions (6)

domain assumption Neutrino flavor states are represented as single-excitation modes: |nu_e> = |100>, |nu_mu> = |010>, |nu_tau> = |001>.
Section II, Eq. (8). This is the mode-entanglement picture used throughout; it treats the one-particle state as an entangled state of three modes.
domain assumption NSI parameters are real-valued.
Table II caption. Complex NSI phases are ignored, which restricts the generality of the results.
domain assumption Earth matter density is constant at 2.8 g/cc along the baseline.
Section II, 'A = 1.01e-13 eV, associated with an Earth's matter density of 2.8 gm/cc'. Realistic density profiles vary with depth.
domain assumption S_AB = Tr(T^T_AB T_AB) > 1 is an if-and-only-if condition for two-setting steerability.
Section III, Eq. (19), attributed to Ref [35]; not re-derived, and may not hold for all two-qubit states.
standard math The evolution operator in matter is given by the Ohlsson-Snellman closed form.
Section II, Eq. (13), citing Ref [39]; accepted standard result.
domain assumption Standard oscillation parameters are fixed to their best-fit values and their uncertainties are not propagated.
Table I; 1 sigma errors are quoted but not used in the plots.

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Cite this review

Pith. "Pith review of Steering in Neutrino Oscillations with Non-Standard Interaction." pith.science (2026). https://pith.science/paper/AQBKXQZK

@misc{pith2026241114234,
  author       = {Pith},
  title        = {Pith review of: Steering in Neutrino Oscillations with Non-Standard Interaction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AQBKXQZK}},
  note         = {Machine review of arXiv:2411.14234}
}

abstract

In this study, we analyze the influence of Non-Standard Interaction (NSI) on steering in three-flavor neutrino oscillations, with a focus on the NO$\nu$A and DUNE experimental setups. DUNE, having a longer baseline, exhibits a more pronounced deviation towards NSI in steering compared to NO$\nu$A. Within the energy range where DUNE's maximum flux appears, the steering value for DUNE shows a $21\%$ deviation from the Standard Model (SM) to NSI for normal ordering (NO), while for inverted ordering (IO), the steering value increases by approximately $15\%$ relative to the SM. We conduct a comparative analysis of nonlocality, steering, and entanglement. Additionally, we express steering in terms of three-flavor neutrino oscillation probabilities and explore the relationship between steering inequality and concurrence.

Figures

Figures reproduced from arXiv: 2411.14234 by the authors.

**Figure 2.** FIG. 2: The plot illustrates the behavior of nonlocality, steering, and [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

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