Revealing hidden nonlocality and preparation contextuality for an arbitrary input Bell inequality

Asmita Kumari; Saikat Patra

REVIEW 3 major objections 5 minor 54 references

Revealing hidden nonlocality and preparation contextuality for an arbitrary input Bell inequality

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read This paper claims that local filtering before the n-bit PORAC measurement reveals hidden nonlocality for every nonzero mixing parameter once n≥6, and preparation contextuality once n≥4.

desk verdict Interesting and likely salvageable, but the general Bell-value formulas contain normalization errors that invalidate the claimed thresholds as written. read the letter →

arxiv 2504.18045 v2 pith:S2TDRRHL submitted 2025-04-25 quant-ph

Asmita Kumari , Saikat Patra This is my paper · ORCID

classification quant-ph PACS 03.65.Ud

keywords hiddennonlocalitypreparationcontextualitylocalfilteringparityobliviousrandomaccesscodeBellinequalitiesmixedentangledstatesquantumcommunicationgamesactivationof

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 asks whether quantum correlations that fall below a Bell threshold can be revived by a local filtering step before measurement. Its setting is the $n$-bit parity-oblivious random access code (PORAC), whose quantum success probability is governed by a Bell functional with two classical bounds: a local bound and a lower preparation-noncontextual bound. For the mixed entangled state $\rho_{2m}=q|\phi_2\rangle^{\otimes m}\langle\phi_2|^{\otimes m}+(1-q)|0\rangle\langle0|\otimes I^{\otimes m}/2^m$, the paper derives the Bell value after local filtering and shows that it exceeds the local bound for every nonzero mixing parameter $q$ once $n\ge6$ (even $n$) or $n\ge7$ (odd $n$), and exceeds the preparation-noncontextual bound for every nonzero $q$ once $n\ge4$ (even $n$) or $n\ge5$ (odd $n$). If right, this means both hidden nonlocality and preparation contextuality can be activated, at arbitrarily small entanglement fraction, across a whole family of Bell inequalities with arbitrarily many inputs.

What carries the argument

The load-bearing machinery is the recursive family of mutually anticommuting Bob observables listed in Table I together with the relation $\sum_{i=1}^{2^{n-1}}(-1)^{s\cdot x_i}A_{n,i}\otimes I=2^{n-1}\sqrt n\, I\otimes B_{n,y}$ from Eq. (12), which ties Alice's $2^{n-1}$ observables to Bob's $n$ observables and reduces the PORAC success probability to the single Bell functional $B_n$. The local filters are tuned to the color-noise structure: choosing $\delta=\xi\sqrt q$ attenuates the $|0\rangle\langle0|$ noise component of $\rho_{2m}$, and the filtered Bell expressions (34)-(35) then contain the population sums $\sum_{v=2}^{\lfloor n/2\rfloor}q/2^{v-1}$ in the numerator. As $\xi\to0$, the normalization $N_d$ and these sums have the same linear scaling in $q$, which is what extends positivity of the violation margin down to arbitrarily small $q$.

What would settle it

For a fixed small mixing parameter such as $q=0.01$, compute the exact Bell value of the filtered state (33) for $n=6$, optimizing over $\xi$, and compare it with the local bound $6\binom{5}{2}=60$; if no choice of $\xi$ yields a value above 60, the all-$q$ nonlocality claim fails. A complementary check is to construct an explicit local hidden variable model for $\rho_{12}$ at $q=0.1$; if no such model exists, the pre-filter state is already nonlocal and the word 'hidden' is not justified.

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Extended reading notes

Core claim

Working with the n-bit PORAC Bell functional $B_n=\sum_{y=1}^n\sum_{i=1}^{2^{n-1}}(-1)^{x_i^y}A_{n,i}\otimes B_{n,y}$, the paper claims two threshold results. After Alice and Bob apply the local filters $F_A=\xi|0\rangle\langle0|+\sum_{j=1}^{2\lfloor n/2\rfloor-1}|j\rangle\langle j|$ and $F_B=\delta|0\rangle\langle0|+\sum_j |j\rangle\langle j|$ with $\delta=\xi\sqrt q$ to the state in Eq. (17), the Bell value of the filtered state (33) is given by Eq. (34) for even $n$ and Eq. (35) for odd $n$. Comparing these with the local bound $n\binom{n-1}{\lfloor(n-1)/2\rfloor}$ and the preparation-noncontextual bound $2^{n-1}$, the paper asserts that the filtered Bell value exceeds the local bound for all $q\in(0,1]$ for even $n\ge6$ and odd $n\ge7$, and exceeds $2^{n-1}$ for all $q\in(0,1]$ for even $n\ge4$ and odd $n\ge5$. The result is presented as the activation of hidden nonlocality and of preparation contextuality for a mixed state that, at small $q$, is below the threshold of the same Bell functional before filtering.

Load-bearing premise

The load-bearing premise is that the unfiltered mixture in Eq. (17) really admits a local hidden variable model for the parameter range where it does not violate the PORAC Bell inequality; the paper asserts this but supplies no explicit local model and no citation to one.

Editorial extensions

If this is right

For the $n$-bit PORAC game, the post-filter success probability beats the preparation-noncontextual bound for every nonzero $q$ once $n\ge4$, so the communication advantage survives arbitrarily small entanglement fraction.
For even $n\ge6$ (odd $n\ge7$), the filtered state violates the local bound for every $q\in(0,1]$, certifying genuine nonlocality rather than only contextuality.
Because the local bound lies above the preparation-noncontextual bound, the family exhibits a parameter window where preparation contextuality is certified while nonlocality is not, making the hierarchy of the two bounds directly visible.
The thresholds hold on the whole open interval $(0,1]$, so the result is not a small-noise effect: the color-noise fraction can be arbitrarily close to one and the filtered state still shows the quantum correlation.

Reading between the lines

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

Going beyond the paper: because the normalization $N_d$ and the numerator sums both scale linearly in $q$ as $\xi\to0$, the violation margins should persist in the $q\to0$ limit for the stated thresholds, suggesting the effect is a property of the observable family more than of the entanglement fraction.
Going beyond the paper: the same filter construction is likely to transfer to Bell functionals built from the recursive anticommuting observables in Table I, and a direct testable extension is to replace color noise with white noise to see whether the thresholds $n\ge6$ and $n\ge4$ move.
Going beyond the paper: until a local model for the unfiltered state is exhibited, the 'hidden' part of hidden nonlocality remains an assumption; the quantitative content that is already demonstrated is the Bell-value comparison after filtering.

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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

First, the headline: this paper has a real gap between its claims and its algebra. The general formulas (34) and (35) are built on a normalization constant that contradicts the explicit n=2 trace, so the n≥6 and n≥4 thresholds are unverified. That said, the stress-test note's specific contradiction for Eq. (27) is wrong: at q=1, ξ=δ=1, Eq. (27) gives 12/√3 = 4√3, matching the paper's own optimal bound, not 14/√3. The n=3 formula survives that check.

What is genuinely new: extending Gisin's n=2 hidden-nonlocality activation to the n-bit PORAC family, with explicit Bell values for filtered states and the claim that local filtering activates nonlocality for any q>0 when n≥6 (even) and preparation contextuality for any q>0 when n≥4. The n=2 and n=3 derivations reproduce direct calculation, and the general idea—filtering a noisy maximally entangled state with a filter that suppresses the |0⟩ component leaves an almost-maximally-entangled state on the remaining subspace—is sound and likely the reason the thresholds exist.

The soft spots are real. (1) The normalization N_d in Eq. (33) is inconsistent with the explicit N2 in Eq. (25): with δ=ξ√q, the trace gives qξ⁴/d, not ξ⁴/(q d). The same error appears in N4 in Eq. (30) and in the general Bell formulas, so all high-n plots and thresholds are suspect. (2) The state in Eq. (17) is claimed to admit a local model for the range where it does not violate this particular Bell inequality, but no local model is given or cited; below-threshold for one Bell functional does not imply locality. Without a local model, this is not activation of hidden nonlocality in the usual sense. (3) Minor: Appendix B uses N2 where N4 belongs in the n=5 derivation.

Who is this for? Quantum foundations readers who work on hidden nonlocality and contextuality. The question is worth asking and the n=2,3 results are solid, but the general formulas need to be re-derived with correct normalization and the local-model claim either proved or downgraded to a detection claim. I would not cite it in its current form, but I would not desk-reject it either. A serious referee should get this; with corrections the result may stand.

Referee Report

3 major / 5 minor

Summary. The paper studies the activation of hidden nonlocality and preparation contextuality in the n-bit parity-oblivious random access code (PORAC) scenario. The authors consider a mixed entangled state of the form q|phi_2>^otimes m<...| + (1-q)|0><0|otimes I^otimes m/2^m, apply local filtering operations, and derive closed-form expressions for the quantum value of the associated Bell functional. They claim that after filtering, nonlocality can be revealed for every nonzero mixedness parameter q when n>=6, and preparation contextuality for every nonzero q when n>=4, with the thresholds inferred from shaded regions in Figs. 1 and 2.

Significance. If the central claim is correct, the paper would provide a scalable demonstration of hidden-nonlocality activation for an arbitrary-input Bell inequality, and would show that preparation contextuality can be activated under weaker assumptions. The manuscript has the virtue of making explicit, checkable predictions: the Bell-value formulas for n=2,3,4,5 are concrete, and the asymptotic xi->0 limits can be evaluated directly. However, the derivations contain operator-norm inconsistencies, a normalization/filter-parameter conflict, and a gap in the local-model justification. These issues affect the quantitative thresholds that are the paper's main new content, so the claims are not yet established in the submitted form.

major comments (3)

[Eq. (12) and Appendix B] Equation (12) is stated as an operator identity, sum_i (-1)^{s.x_i^y} A_{n,i} otimes I = 2^{n-1} sqrt(n) I otimes B_{n,y}. If the A_{n,i} are dichotomic observables, each has operator norm at most 1, so the norm of the left-hand side is at most 2^{n-1}. The right-hand side has norm 2^{n-1} sqrt(n), which is strictly larger for every n>1. Thus Eq. (12) cannot hold as written. The reductions in Appendix B, including Eqs. (B1), (B12), and the induction leading to Eqs. (34) and (35), explicitly rely on Eq. (12), so the derivations of the central Bell-value formulas are not mathematically valid as presented. The authors need to state the correct relation (or prove the stated one under additional assumptions about the A_{n,i}) and re-derive the filtered Bell values.
[Section III.B and Eq. (33)] There is a clear inconsistency between the stated filter relation and the general filtered state. The text in Section III.B defines delta = xi sqrt(q). However, the general normalization in Eq. (33), N_d = [q+(1-q)xi^2](1-1/2^m) + xi^4/(q 2^m), follows from delta = xi / sqrt(q), not from delta = xi sqrt(q). Under the stated relation, the explicit two-qubit normalization in Eq. (25) would become N_2 = (1/2)[q+(1-q)xi^2 + xi^4 q], whereas Eq. (33) with m=1 gives (1/2)[q+(1-q)xi^2 + xi^4/q]; these differ by a factor q^2. The general formulas (34) and (35), and therefore the shaded regions in Figs. 1 and 2, inherit this ambiguity. The authors must specify the correct relation between delta and xi, enforce the filter-norm constraint delta<=1, and re-derive the plots and the any-nonzero-q thresholds.
[Abstract and Section I] The paper repeatedly describes the unfiltered state as 'admitting a local model' and frames the result as activation of hidden nonlocality. However, no local hidden variable model is constructed or cited anywhere in the manuscript. The only evidence offered is that the unfiltered state lies below the local bound of the specific PORAC Bell functional, as in Eq. (19); this does not imply that the state is local. To claim activation of hidden nonlocality, the authors must establish that the unfiltered state admits a local model in the relevant parameter region, or explicitly state the weaker claim that the filter reveals a violation of this particular Bell inequality.

minor comments (5)

[Introduction] The text contains 'q∈[0, 1}' which should be 'q∈[0,1]'.
[Eq. (22)] There is a typo in the concurrence formula: '|det(FAB|' should be '|det(F_B)|'.
[Eq. (16)] The range 'K = 0, 1, 2,... n' should be 'K = 0, 1, ..., 2^m - 1'.
[Reference [35]] The reference entry for Li et al. has a formatting error: 'Phys. Rev. Research 3, 023045 (2021the)' should be 'Phys. Rev. Research 3, 023045 (2021)'.
[Figures 1 and 2] The captions and text state that the shaded regions show the nonlocal and preparation-contextual regions, but the figures themselves do not indicate the values of the fixed parameters (e.g., delta) used in the plots; the delta-relation ambiguity in Section III.B makes it impossible to reproduce the figures from the text alone.

Circularity Check

0 steps flagged · score 2.0 of 10

No construction-level circularity; thresholds come from explicit filtered-state traces compared with external bounds, with only a minor non-load-bearing self-citation.

full rationale

The paper's central claim is that for the filtered state in Eq. (33) the computed Bell values (34)-(35) exceed the local bound (6) for every q>0 when n>=6 (even) or n>=7 (odd), and exceed the preparation-noncontextual bound (9) when n>=4 (even) or n>=5 (odd). These Bell values are obtained by expanding the filtered state explicitly (Eqs. (25), (30), (33)) and evaluating expectation values of the fixed observable sets in Table I; the Alice-observable identity (12) is an algebraic property of those observables imported from published work [29], not a restatement of the target threshold. The local and preparation-noncontextual bounds (6) and (9) are cited external results ([30], [44]) and are not defined in terms of the filtered quantum value being predicted; they are fixed numbers to which the computed curves are compared. No parameter appearing in the thresholds is fitted to the predicted violation; the filter parameter xi is scanned independently and q enters as the state parameter. The pre-filter state is called local, but no LHV model is exhibited; this is an unsupported premise (a correctness concern), not a circular reduction, since the calculation does not define locality as 'satisfies the PORAC Bell bound.' The only self-citation of note is Eq. (6) to the current author's earlier paper [30]; it is a published combinatorial bound, externally checkable and not fitted to the present result, so it does not make the derivation circular. Overall score 2 reflects a minor self-citation, not a found circular step.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim depends on prior bounds for the PORAC Bell functional, on the optimal measurement construction from Ref. [29], and on a stated but unproven local-model property of the mixed state. No constants are fitted to data; the only tunable control is the filter parameter xi, chosen small in the proof.

free parameters (1)

Local filter parameter xi = small, in the limit xi to 0, with delta=xi/sqrt(q) implied by the formulas
The proof of activation for arbitrarily small q relies on taking xi arbitrarily small. The paper treats xi as a free control parameter and does not fit it to data.

assumptions (4)

standard math Local bound of the PORAC Bell functional B_{n,L} <= n * C(n-1, floor((n-1)/2)) (Eq. 6)
Invoked to define nonlocality thresholds; taken from Ref. [30].
standard math Preparation non-contextual bound B_{n,pnc} <= 2^(n-1) (Eq. 9)
Invoked to define preparation contextuality thresholds; taken from Refs. [30,44].
standard math Optimal quantum value B_opt = 2^(n-1) sqrt(n) and the operator relation in Eq. (12) with the Table I observables
The measurement strategy and operator relation are taken from Ref. [29] and used to compute the filtered Bell value.
domain assumption The unfiltered state in Eq. (17) admits a local hidden variable model for q below the PORAC threshold
Assumed so that the post-filter violation counts as hidden nonlocality; no local model is constructed or cited in the paper.

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Pith. "Pith review of Revealing hidden nonlocality and preparation contextuality for an arbitrary input Bell inequality." pith.science (2026). https://pith.science/paper/S2TDRRHL

@misc{pith2026250418045,
  author       = {Pith},
  title        = {Pith review of: Revealing hidden nonlocality and preparation contextuality for an arbitrary input Bell inequality},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/S2TDRRHL}},
  note         = {Machine review of arXiv:2504.18045}
}

abstract

In recent years, the activation of hidden nonlocality for a mixed entangled state, admitting a local model, has gained considerable interest. In this paper, we study the activation of hidden nonlocality and preparation contextuality for a class of mixed entangled states, using local filtering operations. For our demonstration, we consider the two-party (Alice and Bob) one-way communication game known as parity oblivious random access code (PORAC). The quantum success probability of such $n$-bit PORAC solely depends on a Bell functional involving $2^{n-1}$ and $n$ dichotomic measurement settings for Alice and Bob, respectively. Such a Bell functional has two classical bounds, the local and the preparation non-contextual. We show that using local filtering operations on local mixed entangled state, the nonlocality can be revealed for any non-zero value of the mixedness parameter of the entangled state if $n\geq6$. Further, we show that the preparation contextuality, which is a comparatively weaker quantum correlation than nonlocality, can be revealed for any non-zero value of the mixedness parameter of the entangled state if $n\geq 4$.

Figures

Figures reproduced from arXiv: 2504.18045 by the authors.

**Figure 2.** FIG. 2: Shaded region shows preparation contextual region [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** FIG. 3: Di [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

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Inspired by Leibniz’s principle, the concept of non- contextuality in an ontological model emerges from the equiv- alence class of experimental procedures

An ontological model must reproduce the Born rule, i.e., Hence,∀ρ,∀Ek and∀k, R ΛµP(λ|ρ)ξM(k|λ, Ek)dλ = T r[ρEk]. Inspired by Leibniz’s principle, the concept of non- contextuality in an ontological model emerges from the equiv- alence class of experimental procedures. If two preparation procedures P and P′ prepare the same density matrix ρ, then no measur...

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theorem. Besides adding enormous importance in quan- tum foundations both nonlocality and contextuality have been proven to be resources in developing quantum technologies, such as in communication games [3, 4], randomness certifica- tion [5–9], secure quantum key distribution [10–13], witness- ing Hilbert space dimension [14–21] and quantum computa- tion...

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Detailed calculation of Bell expression of odd n For n = 3, following Eq.(12) Bell expression in Eq.(5) reduces to BF 3,Q = 4√ 3 ⟨B3,1⊗ B3,1⟩ +⟨B3,2⊗ B3,2⟩ +⟨B3,3⊗ B3,3⟩ (B12) By comparing the set anti-commuting set of Bob observables in Table.1 for n = 2 and n = 3 we can see that first two terms of the Bell expression,⟨B3,1⊗ B3,1⟩ =⟨B3,2⊗ B3,2⟩ = δξq N2 ...

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