{"id":"493f6eef-33cc-4b20-a9b8-3a4af9541692","arxiv_id":"2504.18045","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"For n-bit parity oblivious random access codes, local filtering reveals nonlocality for any nonzero noise level when n≥6, and preparation contextuality when n≥4.","lead":"Using a family of quantum communication games with arbitrary input size, this paper shows that local filtering can reveal nonlocality in a noisy entangled state for any nonzero mixing level once the game is large enough. It further shows that the weaker effect of preparation contextuality can be revealed for still smaller games, which matters for certifying quantum correlations in the presence of noise.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (27) predicts B_F_3,Q = 14/√3 > 4√3 for the identity filter, contradicting the paper's own optimal quantum bound; the filtered Bell-value formulas are unreliable and the claimed thresholds are unverified.","rationale":"The reader's verdict is CONDITIONAL, and the reader identified the unproven local hidden variable model as the weakest assumption. I agree that the local-model gap is important for the 'hidden nonlocality' framing. However, the more immediately load-bearing problem is internal: the filtered Bell-value formulas, which are the direct basis for the quantitative thresholds, contain algebraic errors. Equation (27) violates the paper's own optimal quantum bound at the identity filter, which is a logical inconsistency independent of any external assumption. This makes the central claims unverified as written. The specific errors (q² vs q, the δ relation, and N_d) are localized and likely repairable; the ξ→0 analysis suggests the thresholds n≥6 and n≥4 may still be correct. Therefore I do not recommend a harsher verdict than the reader's CONDITIONAL, but I would require a corrected derivation and re-plotted figures before acceptance. Agreement is 'partial' because the reader's weakest assumption is the local model, while I see the formula errors as the most immediately decisive concern, with the local model as a second, independent gap.","tokens_in":14159,"tokens_out":34449,"duration_ms":332117,"concrete_test":"Re-evaluate the n=3 Bell expression for the filtered state (25) by directly computing Tr[ρF_2 (A_i ⊗ B_j)] for the Table I observables and compare with Eq. (27). Specifically, at q=1, ξ=1, δ=1, the correct value must equal 4√3, not 14/√3. Then settle the filter relation: if δ = ξ√q, correct N_d in Eq. (33) to q ξ⁴/d; if the intended relation is δ = ξ/√q, state it explicitly and keep ξ⁴/(q d). Re-derive Eqs. (34)-(35) with the corrected normalization and recompute the shaded regions in Figs. 1 and 2 for n=3,4,5,6,7; verify whether the claimed thresholds n≥6 (nonlocality) and n≥4 (preparation contextuality) survive.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim—that after local filtering the PORAC Bell value exceeds the local and preparation-noncontextual bounds for every q>0 when n≥6 or n≥4—rests on the general formulas (34) and (35), which generalize the specific n=2,3,4,5 results (26), (27), (31), (32). The n=3 case already fails an internal consistency check. Setting q=1, ξ=1, δ=1 in Eq. (27) gives B_F_3,Q = 4/√3 [2 + 1 + 0 + 1/2] = 14/√3 ≈ 8.08. With ξ=1, δ=1 the filter is the identity and the state is the maximally entangled two-qubit state, for which the same paper's Eq. (10) gives the optimal quantum value B_opt = 2²√3 = 4√3 ≈ 6.93. A Bell expression cannot exceed its maximum over all quantum states, so Eq. (27) is algebraically wrong. The same bracket error (q² instead of q, with the ξ²δ² term misplaced) propagates to the general odd-n formula (35): at v=1, Eq. (35) reduces to a bracket that differs from Eq. (27), and neither matches direct trace evaluation. In addition, the normalization N_d in Eq. (33) contains ξ⁴/(q d), whereas the explicitly traced N₂ in Eq. (25) yields q ξ⁴/d when δ = ξ√q; the two agree only if the stated δ relation is actually a typo for δ = ξ/√q. The shaded regions in Figs. 1 and 2 are built from these uncorrected expressions. Until the Bell-value formulas are re-derived and checked against direct operator expectation values, the central thresholds are unsubstantiated, even if the ξ→0 asymptotics suggest they might be salvageable.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":14527,"tokens_out":40590,"duration_ms":353083,"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":[{"comment":"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":"Eq. (12) and Appendix B"},{"comment":"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.","section":"Section III.B and Eq. (33)"},{"comment":"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.","section":"Abstract and Section I"}],"minor_comments":[{"comment":"The text contains 'q∈[0, 1}' which should be 'q∈[0,1]'.","section":"Introduction"},{"comment":"There is a typo in the concurrence formula: '|det(FAB|' should be '|det(F_B)|'.","section":"Eq. (22)"},{"comment":"The range 'K = 0, 1, 2,... n' should be 'K = 0, 1, ..., 2^m - 1'.","section":"Eq. (16)"},{"comment":"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)'.","section":"Reference [35]"},{"comment":"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.","section":"Figures 1 and 2"}],"recommendation":"major_revision","confidential_remarks":"The manuscript addresses a relevant problem and contains checkable formulas, but the central derivation is undermined by the operator-norm issue in Eq. (12) and the delta/normalization conflict. The authors should be asked to either supply a correct derivation of Eqs. (34) and (35), or explicitly restrict the claims to the derived expressions. The missing local model should also be addressed. These are fixable within the scope of the paper, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","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.\n\nWhat 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.\n\nThe 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.\n\nWho 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.","headline":"Interesting and likely salvageable, but the general Bell-value formulas contain normalization errors that invalidate the claimed thresholds as written.","tokens_in":15078,"tokens_out":7714,"would_cite":false,"duration_ms":64636,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["03.65.Ud"],"model":"deepseek-v4-flash","headline":"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.","keywords":["hidden nonlocality","preparation contextuality","local filtering","parity oblivious random access code","Bell inequalities","mixed entangled states","quantum communication games","activation of nonlocality"],"falsifier":"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.","tokens_in":13916,"feed_emoji":"⚛️","tokens_out":14789,"duration_ms":129754,"temperature":0.7,"pith_summary":"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.","feed_headline":"Local filters reveal Bell violations at any noise once n ≥ 6","feed_subtitle":"Filtering first makes n-bit PORAC nonlocal for every q from n = 6 and preparation contextual from n = 4.","key_machinery":"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 $q$.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Defines the n-bit PORAC Bell functional, gives its optimal quantum value, and supplies the Alice-Bob observable relation used to evaluate the filtered state.","marker":"[29]"},{"why":"Supplies the local bound $n\\binom{n-1}{\\lfloor(n-1)/2\\rfloor}$ and the comparison between the two classical bounds.","marker":"[30]"},{"why":"Introduces the parity-oblivious constraint and the preparation-noncontextual bound for the PORAC game.","marker":"[44]"},{"why":"Establishes the concept of activating hidden nonlocality by local filtering, which the paper extends.","marker":"[32]"},{"why":"Shows hidden quantum nonlocality revealed by local filters, the direct precedent for the small-n cases.","marker":"[39]"},{"why":"Defines preparation contextuality within the ontological-model framework used to interpret the preparation-noncontextual bound.","marker":"[25]"},{"why":"Provides the family of local filters applied to the color-noise state.","marker":"[49]"}],"fun_headline_variants":["Noise-proof filtering: nonlocality for any q at n≥6, contextuality at n≥4","Filtering first, then Bell violation: n≥6 for nonlocality, n≥4 for contextuality","From local to nonlocal by filtering: n≥6 for any q, n≥4 for contextuality","Any noise, no problem: filtering activates nonlocality (n≥6) and contextuality (n≥4)","Filtering reveals nonlocality at any noise for n≥6 and contextuality for n≥4"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Noise-proof filtering: nonlocality for any q at n≥6, contextuality at n≥4","Filtering first, then Bell violation: n≥6 for nonlocality, n≥4 for contextuality","From local to nonlocal by filtering: n≥6 for any q, n≥4 for contextuality","Any noise, no problem: filtering activates nonlocality (n≥6) and contextuality (n≥4)","Filtering reveals nonlocality at any noise for n≥6 and contextuality for n≥4"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001225,"raw_usage":{"total_tokens":5103,"prompt_tokens":1079,"completion_tokens":4024,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":695,"completion_tokens_details":{"reasoning_tokens":3890}},"tokens_in":695,"tokens_out":4024,"duration_ms":27271,"temperature":1.0,"reasoning_tokens":3890,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T10:29:43.398767+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Revealing hidden nonlocality and preparation contextuality for an arbitrary input Bell inequality","cited_arxiv_id":"2504.18045","evidence_quote":"Defines the n-bit PORAC Bell functional, gives its optimal quantum value, and supplies the Alice-Bob observable relation used to evaluate the filtered state."},{"cited_title":"Bravyi, D","cited_arxiv_id":null,"evidence_quote":"Supplies the local bound $n\\binom{n-1}{\\lfloor(n-1)/2\\rfloor}$ and the comparison between the two classical bounds."},{"cited_title":"Gisin, Hidden quantum nonlocality revealed by local filters, Physics Letters A 210, 151 (1996)","cited_arxiv_id":null,"evidence_quote":"Introduces the parity-oblivious constraint and the preparation-noncontextual bound for the PORAC game."},{"cited_title":"Schr¨odinger, Die gegenw¨artige Situation in der Quanten- mechanik, Naturwissenschaften, 23, 807 (1935)","cited_arxiv_id":null,"evidence_quote":"Establishes the concept of activating hidden nonlocality by local filtering, which the paper extends."},{"cited_title":"Ku, C.-Y","cited_arxiv_id":null,"evidence_quote":"Shows hidden quantum nonlocality revealed by local filters, the direct precedent for the small-n cases."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines preparation contextuality within the ontological-model framework used to interpret the preparation-noncontextual bound."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the family of local filters applied to the color-noise state."}],"review_version":1}