{"id":"66a193d7-6323-48b2-ba4b-4f9d3bfa3e56","arxiv_id":"1908.03124","paper_version":3,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"The paper claims entropic Leggett-Garg inequalities cannot be violated by strong or weak measurements, but the weak-measurement version is contradicted by the paper's own formulas for a specific choice of angles and measurement strength.","lead":"This paper derives entropic versions of the Leggett-Garg inequalities and claims that neither strong nor weak projective measurements can violate them, because the inequalities describe the measurement devices rather than the quantum system. A generalist might read it because many published experiments report violations of Leggett-Garg inequalities, and this paper argues those violations disappear once the middle measurement is included correctly.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Weak-measurement inequality (33) is internally inconsistent: for θ1=π/2, θ2=0, ε=1/2 the paper's own Eqs. (30)-(33) give B'_1≈−0.73, so the claimed no-violation theorem for weak entropic LGIs fails as stated.","rationale":"The central claim has two parts: no violation for strong entropic LGIs and no violation for weak entropic LGIs. The strong part may be salvageable, but the weak part is the paper's advertised extension and is contradicted by its own equations. The reader's identified weakest assumption is precisely the unvalidated H[ε] term in Eq. (33), and the concrete parameter choice θ1=π/2, θ2=0, ε=1/2 gives a negative B'_1. This is not a disagreement with an external consensus; it is an internal algebraic inconsistency. The correct device entropy S(A2) differs from H[ε], so the proof as printed cannot be repaired by a minor wording change; it requires a new derivation and possibly a different inequality. Since the abstract and conclusions explicitly rest on the weak no-violation claim, the paper should not be accepted in its current form. The reader's REJECT verdict remains appropriate, so no adjustment is needed.","tokens_in":92840,"tokens_out":12583,"duration_ms":129964,"concrete_test":"Recompute B'_1(ε) from Eqs. (30)-(33) for θ1=π/2, θ2=0, ε=1/2. If the printed formulas yield B'_1<0, as they do, Eq. (33) is false. Then, if the author responds that H[ε] was meant to denote S(A2)=H[1/2(1+√(1−ε²))], independently check whether S12+S23−S13−S(A2)≥0 holds on a grid over θ1,θ2,ε; this determines whether the weak claim is a typographical error or a genuine gap in the derivation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is after Eq. (32), where the weak-measurement entropic LGI is modified to B'_1(ε)=S12−S13+S23−H[ε]≥0, with the term H[ε] read off the Venn diagram rather than derived. This step is numerically false on the paper's own expressions. For θ1=π/2, θ2=0, ε=1/2: Eq. (30) gives S12=1+H[(1+√3/2)/2]≈1.274; Eq. (31) gives S23=1; Eq. (32) gives S13=1+H[1/2]=2; and H[ε]=H[1/2]=1. Hence B'_1≈−0.726, violating (33) in exactly the weak-measurement regime the theorem is meant to cover. Notably, the text earlier computes S(A2)=H[1/2(1+√(1−ε²))]≈0.274 for ε=1/2, which is not the H[ε]=1 subtracted in (33). Replacing H[ε] by S(A2) would remove this particular counterexample, but that corrected inequality is neither stated nor proven, and all printed formulas and figure labels use H[ε]. Thus the weak no-violation conclusion rests on an internally inconsistent inequality, and the central claim is unsupported as written.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript claims to prove that entropic Leggett-Garg inequalities cannot be violated by either strong or weak sequential quantum measurements. For strong measurements, the author constructs the joint density matrix of three detectors and derives pairwise entropies in Eqs. (20), (25), and (26), concluding that the entropic inequalities B⋆1, B⋆2, and B⋆3 cannot be violated. For weak intermediate measurements, an ancilla rotation parameterized by ε is introduced in Eq. (29), pairwise entropies are stated in Eqs. (30)-(32), and a modified inequality B′1(ε)=S12−S13+S23−H[ε]≥0 is asserted in Eq. (33). The paper concludes that reported violations of entropic Leggett-Garg inequalities are artefacts of using two-point functions that ignore the back-action of the intermediate measurement.","tokens_in":93190,"tokens_out":8928,"duration_ms":86742,"significance":"The question whether entropic Leggett-Garg inequalities can be violated is topical, and the manuscript deserves credit for making its central formulas explicit and checkable: Eqs. (20), (25), (26), and (30)-(32) allow a direct numerical test of the claims. That test, however, is fatal to the main new conclusion. The weak-measurement inequality (33) is contradicted by the paper's own expressions for a simple parameter choice, and the term subtracted in that inequality is not the entropy of the weak detector as computed in the text. The strong-measurement conclusion appears to be repairable, but the proof as printed contains algebraic errors in Eqs. (27)-(28). Because the principal new claim — that weak entropic Leggett-Garg inequalities cannot be violated — is unsupported by the manuscript's own equations, the paper does not establish its central result in its present form.","major_comments":[{"comment":"The claimed weak-measurement inequality is violated by the paper's own formulas. Take θ1=π/2, θ2=0, and ε=1/2. Eq. (30) gives S12 = 1 + H[(1+√3/2)/2] ≈ 1.274. Eq. (31) gives S23 = 1 because its binary-entropy argument is evaluated at p=1. Eq. (32) gives S13 = 1 + H[1/2] = 2. Substituting into the paper's Eq. (33) yields B′1 ≈ 1.274 − 2 + 1 − H[1/2] = −0.726 < 0, directly contradicting the asserted inequality B′1(ε)≥0. This is precisely the weak-measurement regime the theorem is meant to cover. The same parameter choice shows that the subtracted term H[ε]=1 is not the entropy of the weak detector, which the text computes as S(A2)=H[(1+√(1−ε²))/2]≈0.274. Thus the 'read off' of Eq. (33) from Fig. 6b is not a legitimate derivation, and the weak no-violation claim collapses as stated.","section":"§III, Eq. (33) with Eqs. (30)-(32)"},{"comment":"The strong-measurement formulas printed in Eqs. (27)-(28) contain arithmetic errors. Using Eqs. (20), (25), and (26) with θ1=θ2=θ, the exact expression is B⋆1 = S12 + S23 − S13 = 1 + 2H[cos²θ] − H13, not 2H[cos²θ] − H13 as written in Eq. (27). At θ=π/2 the printed expression evaluates to −1, while the exact expression evaluates to 0. Similarly, Eqs. (28) state B⋆2 = B⋆3 = H13, whereas the correct values are B⋆2 = B⋆3 = 1 + H13. These corrections do not by themselves overturn the strong no-violation conclusion, since the corrected expressions are nonnegative and satisfy the required bounds, but the proof as printed is not correct and must be rewritten.","section":"§II, Eqs. (27)-(28)"},{"comment":"The assertion that B′1(ε) is 'guaranteed to be positive owing to strong subadditivity of quantum entropies' is not justified. Strong subadditivity states S(A1A2)+S(A2A3) ≥ S(A1A2A3)+S(A3), which does not directly involve the term −S13 appearing in B′1. Since the Venn diagram in Fig. 6b is introduced without defining its regions in terms of the measured density matrix, the modified inequality is an additional assumption rather than a consequence of the weak-measurement model. This is load-bearing because, as the paper itself notes, the unmodified inequality (9) can be violated for weak measurements; the entire weak-measurement argument rests on the validity of the unproven Eq. (33).","section":"§III, after Eq. (33)"}],"minor_comments":[{"comment":"There are typographical errors: 'cannot be be violated' appears in the abstract and in the introduction, and §III contains 'It is nor permissible' (should be 'not permissible') and 'assmed' for 'assumed'.","section":"Abstract and Introduction"},{"comment":"The notation in Fig. 6b and Eq. (33) labels the subtracted term as H[ε], which conflicts with the text's calculation of the weak-device entropy S(A2)=H[(1+√(1−ε²))/2]. The labels and the algebra need to be made consistent, or a separate symbol must be introduced for the detector entropy.","section":"Fig. 6b and surrounding text"},{"comment":"The tripartite Venn diagram in Fig. 3 is taken from Ref. [33], but the individual regions are not defined in the manuscript. Since the derivation of the entropic inequalities (9)-(11) is presented as an inspection of this diagram, providing explicit definitions of the region entropies would substantially improve verifiability.","section":"Fig. 3 and Sec. II"},{"comment":"The sentence 'Using these entropies in (9) would suggest that weak measurements can certainly violate the entropic Leggett-Garg inequality B⋆1' is imprecise: the numerical violation is parameter-dependent, not a violation for all θ and ε. Clarifying the parameter region would help the reader evaluate the subsequent modification.","section":"§III, unmodified inequality (9)"}],"recommendation":"reject","confidential_remarks":"The central weak-measurement claim is contradicted by the paper's own equations, so the result in its present form cannot be accepted. The strong-measurement proof contains algebraic errors that are locally repairable, but the weak-measurement argument would require a new inequality and a new proof, which goes beyond a routine revision. I found no evidence of improper citation practice; the reliance on the author's companion paper is a separate matter."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe one thing to know: this paper has two halves. The strong-measurement half is a real contribution. It computes the three-time joint density matrix for consecutive projective measurements and shows that the entropic quantity B1* = S12 + S23 − S13 ≥ 0 holds. The point that previous derivations of S13 marginalize over the middle measurement, effectively omitting it, is a fair and important criticism of Refs. [20] and [29]. I believe that half deserves serious attention.\n\nThe weak-measurement half does not survive contact with the paper's own equations. The paper finds that the unmodified B1 can be violated for ε < 1, then reads off a modified inequality B'1(ε) = S12 − S13 + S23 − H[ε] ≥ 0 from a Venn diagram. The extra term is asserted, not derived, and it is not the entropy of the weak detector: the paper itself gives S(A2) = H[(1 + √(1−ε²))/2], which for ε = 1/2 is about 0.355, not H[1/2] = 1. Worse, the proposed inequality is numerically false. Using the paper's Eqs. (30)–(33) at θ1 = π/2, θ2 = 0, ε = 1/2 gives S12 ≈ 1.355, S23 = 1, S13 = 2, so B'1 ≈ 1.355 − 2 + 1 − 1 = −0.645. The stress-test note says −0.726; the arithmetic is slightly off, but the sign is the point. The central no-violation claim for weak measurements is unsupported as stated.\n\nThe rest of the discussion is largely interpretive. The claim that the inequalities describe the measurement devices rather than the quantum system might be right, but the weak proof is the only thing tying it to the entropic case. The citation pattern is reasonable; the self-citations to [1] and [33] are appropriate because [1] is the companion argument and [33] is the source of the Venn-diagram structure. I did not check every line of the strong proof, but nothing there jumps out as wrong.\n\nWho gets value from this? Someone working on entropic temporal inequalities or on the Katiyar experiment would want to read the strong section. The weak section would mislead them if they do not check it.\n\nRecommendation: this is not a desk-reject. It deserves a serious referee because the strong argument challenges published experimental claims and the mistake is instructive. My own verdict is reject in current form: Section III should be withdrawn or replaced by a properly derived inequality. If the author can prove a corrected weak bound, the paper has a chance.","headline":"The strong-measurement half is a legitimate challenge to published entropic LG violations, but the weak half is wrong as written and that is the headline claim.","tokens_in":93671,"tokens_out":5697,"would_cite":false,"duration_ms":58118,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["03.65.Ta"],"model":"deepseek-v4-flash","headline":"Entropic Leggett-Garg inequalities cannot be violated by either strong or weak quantum measurements when the full three-time joint density matrix is used consistently.","keywords":["Leggett-Garg inequalities","entropic inequalities","weak measurements","strong measurements","quantum measurement devices","three-time joint density matrix","entropy Venn diagram","macrorealism"],"falsifier":"Evaluate the paper's own expressions (30)-(32) at $\\theta_1=\\pi/2$, $\\theta_2=0$, $\\epsilon=1/2$, and compute $B'_1(\\epsilon)=S_{12}-S_{13}+S_{23}-H[\\epsilon]$; the result is approximately $-0.73$, which would directly contradict the claim that weak entropic Leggett-Garg inequalities cannot be violated.","tokens_in":92597,"feed_emoji":"⚛️","tokens_out":7577,"duration_ms":72902,"temperature":0.7,"pith_summary":"This paper argues that entropic Leggett-Garg inequalities, the information-theoretic cousins of the standard temporal correlation inequalities, cannot be violated by quantum measurements, whether strong or weak. The apparent violations reported elsewhere are traced to a consistency error: mixing two-time data from runs without the middle measurement with the three-time joint density matrix of consecutive measurements. Once the three detectors are described by one joint density matrix, the inequalities hold, because they constrain the classical measurement devices rather than the quantum system. If correct, this removes a supposed clash between quantum mechanics and macrorealism and shifts the lesson to the unreliability of devices as descriptions of quantum states.","feed_headline":"Weak and strong measurements obey entropic Leggett-Garg bounds","feed_subtitle":"Reported violations vanish when the full three-time joint density matrix is used instead of separate two-time runs.","key_machinery":"The load-bearing object is the entropy Venn diagram for the three measurement devices, whose region sizes are set by the pairwise entropies $S_{12}$, $S_{13}$, and $S_{23}$ computed from the joint density matrix $\\rho_{123}$ of detectors $A_1$, $A_2$, and $A_3$. The diagram converts consistency of $\\rho_{123}$ into non-negativity of combinations such as $S_{12}+S_{23}-S_{13}$. Weak measurements enter through the coupling parameter $\\epsilon$, with the middle ancilla displaced to $\\sqrt{1-\\epsilon^2}|0\\rangle+\\epsilon|1\\rangle$, changing the shared-entropy regions and adding the binary entropy $H[\\epsilon]=-x\\log_2 x-(1-x)\\log_2(1-x)$ to the inequality. The Venn diagram is the bridge from the density matrix to the algebraic form of $B'_1(\\epsilon)$.","core_discovery":"The central claim is that the entropic inequalities $B^\\star_1 = S_{12}+S_{23}-S_{13}\\ge 0$, $B^\\star_2 = S_{12}+S_{13}-S_{23}\\ge 0$, and $B^\\star_3 = S_{13}+S_{23}-S_{12}\\ge 0$ cannot be violated by strong quantum measurements, and that the weak-measurement counterpart $B'_1(\\epsilon)=S_{12}-S_{13}+S_{23}-H[\\epsilon]\\ge 0$ cannot be violated either. The paper computes the three pairwise entropies from the explicit three-device joint density matrix for consecutive measurements on a maximally mixed qubit, with the middle measurement at relative angle $\\theta_1$ and the third at $\\theta_2$. For strong measurements, $B^\\star_1$ is non-negative by convexity, while $B^\\star_2$ and $B^\\star_3$ reduce to a positive entropy. For a weak middle measurement of strength $\\epsilon$, the Venn diagram is modified so that only part of the device entropy is shared with the quantum system, producing the extra $-H[\\epsilon]$ term. The interpretive claim is that reported violations disappear when the full three-time joint probability $P(x,y,z)$ is used, because the inequalities constrain the measurement devices, not the measured system.","pith_inferences":["The weak-measurement case is directly checkable: the modified inequality $B'_1(\\epsilon)$ is read off the Venn diagram rather than derived independently, so evaluating the paper's own expressions at $\\theta_1=\\pi/2$, $\\theta_2=0$, $\\epsilon=1/2$ would decide whether the no-violation claim survives in that region.","The same consistency argument, if extended to temporal or entropic Bell inequalities, suggests that sequential full joint distributions should always satisfy the corresponding entropic bounds, unifying the time and space cases under one principle.","A tomographic experiment that reconstructs $\\rho_{123}$ for three consecutive weak measurements on a single photon or spin could directly test the paper's central distinction by comparing $S_{13}$ from the full state with $S_{13}$ from a run without the middle measurement."],"forward_implications":["If the paper is right, entropic Leggett-Garg inequalities cannot serve as tests of macrorealism; they test whether three measurement devices have a consistent joint description.","Reported violations, including the nuclear-magnetic-resonance experiment cited in the paper, would be artifacts of combining three-time joint data with two-time data from runs without the middle measurement.","A weak or zero-strength middle measurement makes $S_{12}$ and $S_{23}$ tend to one, so the inequalities become trivial rather than violated when the middle measurement is effectively omitted.","The no-violation result extends the author's earlier conclusion for standard Leggett-Garg inequalities to entropy-form inequalities, supporting the view that quantum mechanics consistently describes classical devices."],"supporting_citations":[{"why":"Establishes the companion result for standard Leggett-Garg inequalities and the consistency argument that the middle measurement must be included.","marker":"[1]"},{"why":"Proposes the entropic Leggett-Garg inequality $B^\\star_1$ and claims it can be violated, which is the target the paper corrects.","marker":"[29]"},{"why":"Reports an experimental violation of an entropic Leggett-Garg inequality in nuclear spins, which the paper reinterprets using the full three-time joint distribution.","marker":"[20]"},{"why":"Supplies the three-ancilla entropy Venn diagram and the non-Markovian quantum measurement formalism on which the derivation relies.","marker":"[33]"},{"why":"Used to argue that ideal negative-result measurements disturb the quantum state as much as projective measurements, undercutting non-invasive interpretations.","marker":"[42]"},{"why":"Exemplifies the ideal-negative-result technique whose discarded-half analysis the paper says would still satisfy the inequalities.","marker":"[16]"}],"fun_headline_variants":["Entropic Leggett-Garg inequalities never violated by measurements","Quantum measurements can't beat entropic Leggett-Garg bounds","Entropic Leggett-Garg inequalities immune to weak and strong probes","Why entropic Leggett-Garg violations vanish on closer inspection","Entropic Leggett-Garg inequalities hold for all measurement strengths"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the correct weak-measurement entropic inequality is $B'_1(\\epsilon)=S_{12}-S_{13}+S_{23}-H[\\epsilon]\\ge 0$, with the $-H[\\epsilon]$ term read off the Venn diagram rather than derived; if that premise is false, the weak no-violation result collapses.","fun_headline_variants_meta":{"raw":{"variants":["Entropic Leggett-Garg inequalities never violated by measurements","Quantum measurements can't beat entropic Leggett-Garg bounds","Entropic Leggett-Garg inequalities immune to weak and strong probes","Why entropic Leggett-Garg violations vanish on closer inspection","Entropic Leggett-Garg inequalities hold for all measurement strengths"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000696,"raw_usage":{"total_tokens":3184,"prompt_tokens":1022,"completion_tokens":2162,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":638,"completion_tokens_details":{"reasoning_tokens":2076}},"tokens_in":638,"tokens_out":2162,"duration_ms":15161,"temperature":1.0,"reasoning_tokens":2076,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:24:58.205212+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Evaluate the paper's own expressions (30)-(32) at $\\theta_1=\\pi/2$, $\\theta_2=0$, $\\epsilon=1/2$, and compute $B'_1(\\epsilon)=S_{12}-S_{13}+S_{23}-H[\\epsilon]$; the result is approximately $-0.73$, which would directly contradict the claim that weak entropic Leggett-Garg inequalities cannot be violated.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the companion result for standard Leggett-Garg inequalities and the consistency argument that the middle measurement must be included."},{"cited_title":"Leggett-Garg in- equalities,","cited_arxiv_id":null,"evidence_quote":"Proposes the entropic Leggett-Garg inequality $B^\\star_1$ and claims it can be violated, which is the target the paper corrects."},{"cited_title":"Leggett-Garg in- equality in electron interferometers,","cited_arxiv_id":null,"evidence_quote":"Reports an experimental violation of an entropic Leggett-Garg inequality in nuclear spins, which the paper reinterprets using the full three-time joint distribution."},{"cited_title":"Information-theoretic Bell 9 inequalities,","cited_arxiv_id":null,"evidence_quote":"Supplies the three-ancilla entropy Venn diagram and the non-Markovian quantum measurement formalism on which the derivation relies."},{"cited_title":"Procedure for direct mea- surement of general quantum states using weak measure- ment,","cited_arxiv_id":null,"evidence_quote":"Used to argue that ideal negative-result measurements disturb the quantum state as much as projective measurements, undercutting non-invasive interpretations."},{"cited_title":"Violation of a temporal Bell inequality for single spins in a diamond defect center,","cited_arxiv_id":null,"evidence_quote":"Exemplifies the ideal-negative-result technique whose discarded-half analysis the paper says would still satisfy the inequalities."}],"review_version":1}