{"id":"b63488ed-249a-4f6a-81f7-74bae5ff7473","arxiv_id":"1908.02886","paper_version":2,"verdict":"REJECT","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"The paper argues that Leggett-Garg inequalities cannot be violated by any projective measurement when correlators are defined on measurement device outcomes, and that experimental violations arise from inconsistent assumptions about non-invasive measurability.","lead":"Christoph Adami re-analyzes sequential quantum measurements and claims that Leggett-Garg inequalities are never violated, because earlier violations mixed invasive and non-invasive assumptions. The claim challenges a large body of experiments, but the analysis depends on redefining the measured quantities as device outcomes rather than system properties.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Weak-measurement correlators drop the non-orthogonality of the pointer states; Eq. (21) is false, so the proof that weak projective measurements cannot violate LGIs is unsupported.","rationale":"The load-bearing link is clear: the abstract's 'any projective measurement' and 'never violated, no matter how fuzzy' claims require the weak-measurement derivation to be correct. That derivation fails at the exact step where the paper forms the reduced states of the measurement devices: it treats |0>2 and |ε>2 as orthogonal even though the paper itself defines ⟨0|ε⟩ = √(1−ε^2). This is an internal inconsistency, not merely a disagreement with an external consensus. The reader's specific wording that the system is 'completely dephased' at ε=0 is not accurate—at ε=0 Eq. (13) reduces to |+>|0>1|0>2, with no dephasing—but the reader's broader identification of the weak-measurement model as the weak point is correct and lands at a deeper level. The paper also leaves key inequalities as 'straightforward to show' and contains misprints, but those are secondary; the dropped pointer-overlap terms are the decisive flaw. If the corrected correlators still obey the inequalities, the conclusion might survive but would need a new proof; if not, the headline claim is false. Either way, the reader's REJECT verdict remains appropriate, so no verdict adjustment is needed.","tokens_in":14264,"tokens_out":26640,"duration_ms":253010,"concrete_test":"Recompute K13 from Eq. (18) without dropping the overlap <0|ε> = √(1−ε^2). Concretely, evaluate ρ13 = Tr_{system,2}|Ψ3><Ψ3| and K13 = Tr(ρ13 σz⊗σz), then compare with Eq. (21) at ε=0 and θ1=θ2=π/4: Eq. (21) gives 1/2, while the state (18) gives cos(π/2)=0. If the recomputation yields 0, Eq. (21) is false and the weak-measurement no-violation proof must be redone. As a second step, scan the corrected B1, B2, B3 over θ1, θ2 in [0,π] and ε in [0,1] to see whether the central claim survives with the corrected correlators.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central new claim, that weak projective measurements cannot violate the Leggett-Garg inequalities, rests on Eqs. (20) and (21), and these equations are internally incorrect. From the paper's own state after the first weak measurement and the second CNOT, Eq. (18), the first pointer appears in superpositions such as cos(θ1/2)cos(θ2/2)|0>2 − sin(θ1/2)sin(θ2/2)|ε>2. Because |ε>2 is defined as √(1−ε^2)|0>2 + ε|1>2, the states |0>2 and |ε>2 overlap: <0|ε> = √(1−ε^2). Tracing out the system and the first pointer therefore produces cross terms proportional to √(1−ε^2). Equation (19) keeps only the diagonal pointer terms |0>2<0| and |ε>2<ε|, dropping exactly those interference terms. Consequently Eq. (20) is missing −√(1−ε^2) sinθ1 sinθ2, and Eq. (21) is false. The correct value is K13 = cosθ1 cosθ2 − √(1−ε^2) sinθ1 sinθ2, which equals cos(θ1+θ2) at ε=0 and equals cosθ1 cosθ2 only in the strong limit ε=1. This also makes the text self-contradictory: the paper says cos(θ1+θ2) would follow if ε=0, while Eq. (21) claims an ε-independent cosθ1 cosθ2. Since Eqs. (22)–(24) and (31)–(33) are derived from these correlators, the weak-measurement no-violation proof is invalid as written. The strong-measurement discussion may restate earlier critiques, but the weak-measurement claim is the paper's new contribution and is not established by its calculation.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper claims that Leggett-Garg inequalities cannot be violated by any projective measurement, strong or weak, and argues that previously reported violations (e.g., Knee et al. 2012, Goggin et al. 2011) are artifacts of mixing invasive and non-invasive assumptions. The author introduces a model with three binary measurement devices, derives correlation functions K12, K23, K13 from a sequence of one weak and one strong measurement on a qubit, and concludes that the LGI combinations B1, B2, B3 are always bounded by 1 for any measurement strength and any initial state.","tokens_in":14654,"tokens_out":18575,"duration_ms":158450,"significance":"If the central claim were correct, the paper would overturn a large body of experimental and theoretical work on Leggett-Garg violations and would support the view that quantum mechanics adequately describes macroscopic objects. However, the new contribution—the no-violation result for weak measurements—rests on an incorrect reduced-density-matrix calculation. The strong-measurement discussion is largely consistent with earlier critiques of non-invasive measurability, but it is not new, and the explanatory framework based on an assumed joint distribution is circular. The paper does not provide a valid derivation of the weak-measurement correlators, so the headline result is not established.","major_comments":[{"comment":"The derivation of K23 and K13 drops the off-diagonal elements of the pointer state. From the paper's own Eq. (18), the branch containing |θ2>|0>3 has device 2 in the superposition cos(θ1/2)cos(θ2/2)|0>2 − sin(θ1/2)sin(θ2/2)|ε>2. Because <0|ε> = √(1−ε^2) ≠ 0, the reduced density matrix ρ23 obtained by tracing out the quantum system contains cross terms |0>2<ε| and |ε>2<0|. Equation (19) omits these terms, effectively treating |0>2 and |ε>2 as orthogonal. Including them gives K23 = (1−ε^2)cosθ1cosθ2 + ε^2cosθ2 − √(1−ε^2)sinθ1sinθ2 and K13 = cosθ1cosθ2 − √(1−ε^2)sinθ1sinθ2 for the preparation |+>. Consequently Eq. (21) is false, and the inequalities (22)–(24) and (31)–(33) are not derived from the model.","section":"Eqs. (18)–(21)"},{"comment":"The text states that K13 = cos(θ1+θ2) would follow if ε=0, but Eq. (21) itself gives K13 = cosθ1cosθ2 for every ε, including ε=0. This internal contradiction shows that the derivation of K13 is not reliable. The contradiction is not merely semantic: the correct calculation for ε=0 in the model yields cosθ2 (since the first measurement is not performed), not cos(θ1+θ2), so the paper's interpretation of the standard LGI expression is itself muddled.","section":"Comment after Eq. (21)"},{"comment":"The weak-measurement state is not derived from the stated interaction. The paper defines U1 = e^{-iH(g)} with H = gPθ⊗σ_y, for which the ancilla evolves to |ε> on the |θ1> branch and stays at |0> on the |θ̄1> branch. The replacement in Eq. (13) of |1>2 by |ε>2 instead places |ε> on the |θ̄1> branch, since Eq. (13) is the strong-CNOT state with the flip on |θ̄1>. Thus the model is not the stated weak measurement, and the claim that the conclusions apply to 'weak projective measurements' is not supported by the model's dynamics.","section":"Eq. (13) and the interaction Hamiltonian"},{"comment":"The paper asserts that 'it is straightforward to show' that the inequalities (31)–(33) cannot be violated for any state preparation or any measurement strength, but no proof is provided. Given that the correlators feeding into these inequalities are incorrect, the assertion is unsupported. Even within the paper's own framework, the derivation of these bounds would require an explicit demonstration that the right-hand sides never exceed 1 for all θ1, θ2, α, β, and ε.","section":"Inequalities (31)–(33)"}],"minor_comments":[{"comment":"The expression for K12 contains repeated and incorrectly signed terms; it should be K12 = P(+++) + P(++−) − P(+−+) − P(+−−) − P(−++) − P(−+−) + P(−−+) + P(−−−).","section":"Eq. (2)"},{"comment":"Equation (18) contains stray parentheses and missing kets (for example '⟩|0⟩3' and '⟩|0⟩2'), and Eq. (19) has an apparent index typo in the second term where |0⟩2⟨0| likely should be |0⟩3⟨0|. These typographical errors make the calculation difficult to follow.","section":"Eqs. (18) and (19)"},{"comment":"The author of reference [4] is spelled 'Ballentine' (L. E. Ballentine), not 'Ballantine' as in the text and reference list.","section":"Reference [4]"},{"comment":"The statement that K13 'will depend on ε for arbitrary preparations' is not demonstrated and is contradicted by the special case β=0 in Eq. (27), where the preparation-dependent term vanishes but the calculation from Eq. (18) still contains a √(1−ε^2)sinθ1sinθ2 term.","section":"General correlators, Eqs. (25)–(27)"}],"recommendation":"reject","confidential_remarks":"The paper's central new result, the no-violation claim for weak measurements, is invalid as written because the reduced density matrix in Eq. (19) drops the non-orthogonality of the pointer states. The corrected correlators differ from Eqs. (20) and (21) by terms proportional to √(1−ε^2)sinθ1sinθ2, so all subsequent inequalities are not established. The weak-measurement model is also not faithfully derived from the stated Hamiltonian. In my assessment this is a load-bearing error that cannot be fixed by local revision; the manuscript would need a completely new derivation of the weak-measurement correlators and a re-evaluation of the conclusions. I recommend rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, the paper's new claim—that weak projective measurements cannot violate Leggett-Garg inequalities—is not established. The calculation that produces Eqs. (20) and (21) drops off-diagonal terms between the pointer states |0>2 and |ε>2, and those terms are real. Working from the paper's own Eq. (18), the first pointer is left in superpositions such as cos(θ1/2)cos(θ2/2)|0>2 − sin(θ1/2)sin(θ2/2)|ε>2. Because <0|ε> = √(1−ε²), tracing out the system leaves cross terms proportional to √(1−ε²). Equation (19) keeps only |0><0| and |ε><ε|, so the resulting correlators are missing −√(1−ε²) sinθ1 sinθ2. The correct K13 is cosθ1 cosθ2 − √(1−ε²) sinθ1 sinθ2, not cosθ1 cosθ2; K23 picks up the same correction. That invalidates Eqs. (20)–(24) and (31)–(33). The paper's own Eq. (27) is inconsistent with Eq. (21) for the |+> preparation, which is a red flag.\n\nSecond, the strong-measurement part is fine but not new. The point that LGI \"violations\" come from assuming non-invasiveness (using K13 = cos(θ1+θ2) while measuring K12 and K23 invasively) is exactly what Ballantine, Peres, and Dicke said, and the paper says so. The explicit device-outcome calculation for strong measurements is a useful pedagogical restatement.\n\nOn the weaker side: the title overclaims. The paper only analyzes a particular model of projective measurements on a qubit; it doesn't show that no quantum measurement can violate LGIs. The analysis of Knee et al. is suggestive but not a proof that their data would show no violation if re-analyzed. There are also misprints in Eq. (2) and Eq. (19), and the derivations of (22)–(24) are asserted rather than shown.\n\nThe weak-measurement model itself is not the problem. The system is not \"fully projected\" for any ε; the issue is purely the dropped interference terms in the pointer trace.\n\nWho gets value: someone working on LGI and macrorealism will find a clear restatement of the non-invasiveness critique and a reasonable device-outcome framework. They should not cite the weak-measurement no-violation claim until it's fixed.\n\nRecommendation: this deserves a serious referee only if the editor is willing to demand a major rewrite. The error is concrete and fixable—redo the trace correctly—but as written the central new result does not follow. If the bar is correctness of the main claim, desk reject; if the bar is whether a competent author can repair it, send it out.","headline":"The paper's weak-measurement proof is invalid: the correlator calculation drops pointer-state interference terms, so the main new claim is unsupported; the strong-measurement part is a clean restatement of known critiques.","tokens_in":15181,"tokens_out":20413,"would_cite":false,"duration_ms":174666,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["03.65.Ta"],"model":"deepseek-v4-flash","headline":"Leggett-Garg inequalities cannot be violated by any projective measurement, strong or weak; reported violations are artifacts of mixing invasive and non-invasive assumptions.","keywords":["Leggett-Garg inequalities","projective measurements","weak measurements","non-invasive measurability","macrorealism","temporal correlations","measurement invasiveness","qubit measurements"],"falsifier":"Compute the three correlators for a weak measurement modeled by the full unitary $U=e^{-igP_\\theta\\otimes\\sigma_y}$, keeping the system's coherent superposition instead of replacing the flipped ancilla by $|\\epsilon\\rangle$; if for any $\\epsilon\\in(0,1)$ the combination $K_{12}+K_{23}-K_{13}$ exceeds 1, the paper's no-violation claim for weak projective measurements fails. Experimentally, re-analyze the kept and discarded outcome sets of a published 'interaction-free' Leggett-Garg experiment, since the paper predicts both sets give the same correlators and the same apparent violation.","tokens_in":14030,"feed_emoji":"⚛️","tokens_out":10858,"duration_ms":110166,"temperature":0.7,"pith_summary":"The paper claims that Leggett-Garg inequalities—bounds on correlations between consecutive measurements of the same quantum system—cannot be violated by any projective measurement, strong or weak. It derives explicit correlation functions for a sequence of three measurements on a qubit and shows that all three standard inequalities are bounded by 1 for every measurement strength and every initial state. The apparent violations reported in experiments are attributed to an inconsistent use of non-invasive measurability: the middle measurement is treated as absent ($\\epsilon=0$) in one correlator but as fully projective ($\\epsilon=1$) in another. Weak projective measurements also fail, the paper argues, because although the measured quantum system is not fully projected, the measurement devices are. If the claim holds, the long-standing worry that quantum mechanics fails to describe macroscopic objects loses its main experimental support.","feed_headline":"Leggett-Garg inequalities survive every projective measurement","feed_subtitle":"A new derivation says reported violations mix invasive and non-invasive assumptions, not a failure of quantum mechanics.","key_machinery":"The load-bearing object is the joint wave function of a quantum system plus the ancillas that record each measurement. A strong projective measurement is implemented by a controlled-NOT operation that flips the ancilla when the system is in one basis state; a weak projective measurement is the same gate with the flip replaced by a small rotation, leaving the ancilla in $|\\epsilon\\rangle_2=\\sqrt{1-\\epsilon^2}|0\\rangle_2+\\epsilon|1\\rangle_2$. Tracing out the quantum system leaves reduced density matrices for the measurement devices, and the correlators $K_{ij}$ are read off as $\\operatorname{Tr}(\\rho_{ij}\\sigma_z\\otimes\\sigma_z)$. The argument works because the Leggett-Garg combinations are built from the diagonal elements $P(xyz)$ of a joint probability distribution over three binary outcomes, and nonnegative probabilities automatically bound those combinations by 1.","core_discovery":"The paper's central claim is that the Leggett-Garg inequalities, $B_1=K_{12}+K_{23}-K_{13}\\le 1$ and its two cyclic variants, are never violated by any projective measurement of a qubit, at any measurement strength and for any initial state. Using a unitary measurement model in which a strong measurement is a controlled-NOT flip of an ancilla and a weak measurement rotates the ancilla to $|\\epsilon\\rangle_2=\\sqrt{1-\\epsilon^2}|0\\rangle_2+\\epsilon|1\\rangle_2$, the author derives the correlators $K_{12}=(|\\alpha|^2-|\\beta|^2)(1-\\epsilon^2)+\\epsilon^2\\cos\\theta_1$, $K_{23}=(|\\alpha|^2-|\\beta|^2)(1-\\epsilon^2)\\cos\\theta_1\\cos\\theta_2+\\epsilon^2\\cos\\theta_2$, and $K_{13}=\\cos\\theta_1\\cos\\theta_2-2\\sqrt{1-\\epsilon^2}|\\alpha||\\beta|\\sin\\theta_1\\sin\\theta_2$. Substituting these into the Leggett-Garg combinations yields expressions bounded above by 1 for all $\\epsilon\\in[0,1]$ and all $\\alpha,\\beta$. The apparent violations reported in the literature follow from using $\\epsilon=0$ for the middle measurement when computing $K_{13}$ while using $\\epsilon=1$ for the same measurement when computing $K_{12}$ and $K_{23}$.","pith_inferences":["A natural extension of the paper's diagnosis is that any temporal inequality built from correlators obtained under different measurement-strength assumptions—entropic Leggett-Garg bounds, temporal Bell inequalities, or no-signaling-in-time conditions—should show the same pattern of spurious violation when $\\epsilon=0$ and $\\epsilon=1$ data are mixed.","The decisive test of the weak-measurement claim would be a model that keeps the system's coherence proportional to the coupling; if Leggett-Garg violations reappear there, the paper's conclusion would be specific to its fully dephasing weak-measurement scheme rather than to all projective measurements.","The paper's broader moral, that temporal correlation bounds constrain classical records rather than quantum evolution, suggests a route to no-violation theorems for higher-dimensional systems and longer measurement sequences using the same positivity-of-probabilities argument."],"forward_implications":["Every reported experimental violation of a Leggett-Garg inequality would be explained as an artifact of combining a non-invasive assumption for one correlator with an invasive measurement for the others, rather than as evidence against macrorealism.","The three-point correlator for consecutive strong measurements is $K_{13}=\\cos\\theta_1\\cos\\theta_2$, not $\\cos(\\theta_1+\\theta_2)$; experiments that measure all three correlators directly can check this prediction.","Quantum mechanics would remain an adequate description of macroscopic objects, removing the original motivation for doubting it on Leggett-Garg grounds.","Weak measurements cannot rescue Leggett-Garg violations because the measurement devices are fully projected even when the measured system is not; therefore weak-measurement tests are subject to the same non-invasiveness criticism.","The inequalities should be read as constraints on classical measurement records, not on the quantum system: classical objects cannot adequately describe quantum objects, not vice versa."],"supporting_citations":[{"why":"Defines the Leggett-Garg inequalities and the macrorealism and non-invasive-measurability assumptions that the paper targets.","marker":"[3]"},{"why":"An early argument that non-invasive measurability contradicts quantum mechanics; the paper's explanation of perceived violations is an explicit version of this point.","marker":"[4]"},{"why":"An independent early objection that non-invasive measurement is not possible for quantum flux, supporting the claim that invasiveness is the source of apparent violations.","marker":"[5]"},{"why":"The prominent 'ideal non-invasive' experiment the paper reinterprets; its kept and discarded data sets are the concrete case where mixing $\\epsilon=0$ and $\\epsilon=1$ correlators occurs.","marker":"[6]"},{"why":"Proposes decoherence or the impossibility of sharp measurements as explanations for easy strong-measurement violations; the paper argues neither is needed.","marker":"[17]"},{"why":"The weak-measurement experiment that reportedly violates Leggett-Garg inequalities; the paper classifies it as a parallel CHSH-type setup rather than a consecutive Leggett-Garg test.","marker":"[18]"},{"why":"An experimental observation that the three-time joint probability cannot reproduce two-time marginals, used as evidence that non-invasiveness, not the grand probability, is the illegitimate assumption.","marker":"[22]"}],"fun_headline_variants":["No projective measurement can violate Leggett-Garg","Leggett-Garg inviolable by any projective measurement","Weak projective measurements also respect Leggett-Garg","Leggett-Garg violations traced to flawed non-invasiveness","Every projective measurement obeys Leggett-Garg"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument depends on a model in which every weak measurement completely destroys the measured system's original superposition—even at zero strength, where no measurement actually occurs; if a genuine weak measurement leaves the system mostly intact, the no-violation claim for weak projective measurements may collapse.","fun_headline_variants_meta":{"raw":{"variants":["No projective measurement can violate Leggett-Garg","Leggett-Garg inviolable by any projective measurement","Weak projective measurements also respect Leggett-Garg","Leggett-Garg violations traced to flawed non-invasiveness","Every projective measurement obeys Leggett-Garg"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000319,"raw_usage":{"total_tokens":1808,"prompt_tokens":960,"completion_tokens":848,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":576,"completion_tokens_details":{"reasoning_tokens":772}},"tokens_in":576,"tokens_out":848,"duration_ms":8488,"temperature":1.0,"reasoning_tokens":772,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:31:54.949060+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the three correlators for a weak measurement modeled by the full unitary $U=e^{-igP_\\theta\\otimes\\sigma_y}$, keeping the system's coherent superposition instead of replacing the flipped ancilla by $|\\epsilon\\rangle$; if for any $\\epsilon\\in(0,1)$ the combination $K_{12}+K_{23}-K_{13}$ exceeds 1, the paper's no-violation claim for weak projective measurements fails. Experimentally, re-analyze the kept and discarded outcome sets of a published 'interaction-free' Leggett-Garg experiment, since the paper predicts both sets give the same correlators and the same apparent violation.","supporting_citations":[{"cited_title":"Violation of a Leggett-Garg inequality with ideal non-invasive measurements,","cited_arxiv_id":null,"evidence_quote":"The prominent 'ideal non-invasive' experiment the paper reinterprets; its kept and discarded data sets are the concrete case where mixing $\\epsilon=0$ and $\\epsilon=1$ correlators occurs."}],"review_version":1}