{"id":"d9cd580e-716b-4038-8713-a85498bf16b9","arxiv_id":"2507.21221","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Wigner's Friend effects survive in a quantum-Darwinism decoherence model, but they are confounded by classical ignorance and suppressed as the Friend grows larger.","lead":"Researchers studied Wigner's Friend thought experiments with a decohering environment using quantum Darwinism, treating the Friend as a small collection of qubits that records information about a quantum system. They found that genuine Wigner's Friend disagreements can still appear, but they shrink as the Friend grows, and extended versions that could violate local friendliness are severely restricted.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The Δ≫ε criterion is undermined: ε (Eq. 20) is a bias between Helstrom errors rather than the state-discrimination error, and M_L (Eq. A6) is a classical parity test on two noisy copies; the claimed genuine WF effect is classical, not quantum.","rationale":"The reader's weakest assumption was that the Friend's optimal SBS assignment presumes knowledge of the exact conditional states. I agree that is problematic, but the more load-bearing issue is that even granting that knowledge, the reported 'genuine WF effect' is not a quantum effect. The paper's own definitions require a True WF-Type Effect to arise from coherences in Wigner's state that the Friend lacks (Sec. II B, Table II). Here the pinching map removes all inter-branch coherences (σ=0 in Eq. 13), and the post-measurement state (Eq. 17) is a separable mixture of product states. The Lab measurement M_L (Eq. A6) is literally a parity check of the Helstrom readouts of F and E. The disagreement Δ equals the probability that those two readouts differ, a purely classical quantity generated by two noisy channels reading the same classical bit. The comparison to ε does not rescue the claim, because ε is the bias between the two Helstrom error probabilities, not their magnitude; it can vanish even when Wigner misreads the Friend 20% of the time. Thus the numerical observation Δ≫ε is an artifact of combining two noisy readouts and comparing against a bias, not evidence of coherence or of a WF paradox. The central claim and the 'novel form of WF effect' in the abstract and conclusions are therefore unsupported. The EWFS part (modified LF inequalities, numerical non-objectivity) is more robust, but the main advertised result fails, so the verdict should be REJECT rather than CONDITIONAL.","tokens_in":25887,"tokens_out":23484,"duration_ms":275497,"concrete_test":"Re-run the WF-QD numerics (Sec. II D, Appendix A) for NF,NE ∈ {2,3,4,5} and p0=p1=0.5. For each GUE sample, compute: (a) the true Helstrom error P_err = 1 − ½(e0+e1); (b) the classical disagreement Δ_class = ½[e0(1−f0)+(1−e0)f0 + e1(1−f1)+(1−e1)f1]; (c) ε = ½|e0−e1| and Δ = |P^W(0)−P^F(0)|. Check whether Δ = Δ_class to numerical precision (it should, since M_L is a parity check) and whether P_err is comparable to Δ while ε is tiny. Also build a classical simulation with latent bit i (p=0.5) and binary asymmetric channels with success probabilities e_i, f_i; if it reproduces P^W(0) and Δ, the effect is exhausted by classical noise, not a genuine Wigner's-Friend effect.","verdict_should_be":"REJECT","load_bearing_attack":"The central claim in Sec. II D is that Δ ≫ ε for the measurement M_L (Eqs. 22-23, Fig. 4) demonstrates a genuine Wigner's-Friend effect. This criterion is not sufficient, for two reasons. First, ε is not the state-discrimination error. For p0=p1, Eq. (24) gives ε = |P^W(0) − P^F(0)| = ½|e0 − e1|, where e_i = Tr(Π_F^i ρ_F^i). It measures only the asymmetry between the two Helstrom success probabilities. Symmetric noise (e0≈e1) gives ε≈0 regardless of how poorly Wigner can read the Friend: if e0=e1=0.8, ε=0 while the actual error is 20%. The reported ε∈[1e-5,0.012] is therefore compatible with large readout error. Second, M_L (Eq. A6) is a parity check on the Helstrom outcomes of F and E. Because the pinched post-measurement state (Eq. 17) is a separable mixture over the pointer outcome i of product states, the probability of disagreement is Δ = Σ_i p_i [e_i(1−f_i)+(1−e_i)f_i]. This is exactly the error probability of two noisy classical channels reading the same classical bit i. The pinching map sets σ=0 in Eq. (13), so no inter-branch coherence survives; the state admits a classical hidden-variable model. The Friend's assignment (Eq. 18) simply replaces the noisy states by noiseless Helstrom projectors; the resulting disagreement is a classical model-misspecification, not the 'coherence between Friend and environment' claimed in Sec. IV. Hence Δ ≫ ε does not establish a genuine WF effect.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper models Wigner's Friend (WF) scenarios using a quantum-Darwinism (QD) framework, in which the Friend's measurement is a unitary equilibration process governed by a broadcasting Hamiltonian. After the measurement, the lab state is a pinched, SBS-like state (Eq. 17). The authors define a criterion for a 'genuine WF effect' by comparing the disagreement Δ between Wigner and the Friend for a carefully chosen measurement M_L^0 (Eq. A6) with a parameter ε representing the inaccuracy of Wigner's readout of the Friend's outcome (Eq. 20). Numerically, they report Δ≈0.3–0.4 while ε∈[10^-5,0.012], which they interpret as evidence for a novel WF effect in the presence of a decohering environment. The paper also analyzes extended WF scenarios, showing that the broadcasting-Hamiltonian model yields separable post-measurement states (so LF inequalities cannot be violated), and that non-objectivity modifies the LF inequalities to a bound 2+4ε. The central positive claim of a novel WF effect in the WF-QD model is the focus of this report.","tokens_in":26245,"tokens_out":6755,"duration_ms":70612,"significance":"If the claimed novel WF effect in Sec. II D were valid, it would provide an interesting bridge between quantum Darwinism and Wigner's Friend scenarios, and the EWFS restrictions (Sec. III B, Eq. 40) are a useful quantitative result that connects state-discrimination error to the violation of Local Friendliness. The paper is clearly written and the numerical work is extensive, with well-documented methods (Appendices A and C). However, the main numerical claim is undermined by the definition of ε and by the classical nature of the chosen measurement M_L^0. The EWFS part, which is more robust, could form a solid but more modest contribution; the 'novel WF effect' as presented is not demonstrated by the reported evidence.","major_comments":[{"comment":"The parameter ε defined in Eq. (20) is not the state-discrimination error. For p0=p1, Eq. (25) shows that P^W(i=0)=p0(1+e0−e1), so ε=|P^W(0)−P^F(0)|=½|e0−e1|. This is the difference between the two Helstrom success probabilities, not the probability of error. If the noise is symmetric (e0≈e1), ε≈0 even when the actual readout error is large (e.g., e0=e1=0.8 gives ε=0 with a 20% error). Therefore the reported values ε∈[10^-5,0.012] do not guarantee that Wigner can accurately read the Friend's outcome, and the criterion Δ≫ε in Eq. (23) is insufficient to establish a genuine WF effect.","section":"Sec. II D, Eqs. (20) and (24)"},{"comment":"The measurement M_L^0 is a parity check on the Helstrom outcomes of the Friend and the environment. Because the pinched post-measurement state in Eq. (17) is a separable mixture over the pointer outcome i of product states, the probability of disagreement Δ for M_L^0 equals Σ_i p_i [e_i(1−f_i)+(1−e_i)f_i], which is exactly the disagreement probability of two noisy classical channels reading the same classical bit i. No inter-branch coherence survives the pinching map (σ=0 in Eq. (13)), so the state admits a classical hidden-variable model. The claimed 'coherence between Friend and environment' mentioned in Sec. IV is not present in the model; the disagreement arises from the Friend's assignment of noiseless projectors (Eq. 18) instead of the actual noisy states, which is a classical model-misspecification.","section":"Sec. II D, Eq. (A6)"},{"comment":"The Friend's optimal SBS-state assignment in Eq. (18) is constructed from the Helstrom projectors Π_F^(i) and Π_E^(i) that optimally discriminate the true post-measurement states ρ_F^(i) and ρ_E^(i). Wigner's j-measurement M_L^0 in Eq. (A6) is built from exactly these same projectors. This creates a circularity: the large Δ reported for M_L^0 measures, in part, the mismatch between the Friend's assumed perfectly distinguishable states and the actual noisy states, while both the Friend's assignment and Wigner's measurement are tailored to the true states. A real Friend, who by assumption has limited access to the environment, would not know the exact ρ_E^(i), and her assignment would differ; the reported comparison is therefore not a fair representation of the WF disagreement in a realistic setting.","section":"Sec. II C, Eq. (18) and Appendix A 2"}],"minor_comments":[{"comment":"The definition ε:=|P^W(i)−P^F(i)| does not specify which outcome i is used; the numerical results later refer to i=0. The formula should be stated with an explicit index, e.g., ε=|P^W(0)−P^F(0)|.","section":"Sec. II C, Eq. (20)"},{"comment":"The claim of an 'emergence of classicality' with increasing NF is based on visual trends and best-fit lines that are only guides to the eye; the authors should provide a more quantitative assessment, especially since Appendix C shows the opposite trend for p0≠p1.","section":"Fig. 4 and Sec. II D"},{"comment":"The parameter ε defined in Eq. (39) for the EWFS case is a genuine average state-discrimination error (1 − Σ_c p(c) Tr(Π_(c)_C ρ_(c)_C)), which is conceptually different from the ε defined in Eq. (20) as |P^W(i)−P^F(i)|. This inconsistency in notation should be clarified.","section":"Sec. III B, Eq. (39)"},{"comment":"The authors note that their use of 'non-objectivity' is non-standard, but the term is still potentially confusing. A brief sentence explaining the relationship to the standard QD notion of objectivity (and why the weaker notion is sufficient for their argument) would improve readability.","section":"Sec. II C, around Eq. (14)"},{"comment":"The POVM elements M_L^0 and M_L^1 are not normalized projectors but sums of product POVM elements; the text could state explicitly that they form a valid POVM (i.e., M_L^0 + M_L^1 = 1_L) and that the individual Helstrom elements are projectors in the two-outcome case considered.","section":"Appendix A 2, Eq. (A6)"}],"recommendation":"major_revision","confidential_remarks":"The main positive claim of the paper—a 'novel WF effect exploiting coherence between Friend and environment'—is not supported by the current evidence. The ε criterion is not a state-discrimination error, and M_L^0 is a classical parity test on two noisy classical channels; the large Δ is a classical model-misspecification. This is a load-bearing issue, not a presentation issue. The authors would need to either find a measurement that genuinely exploits quantum coherences in the model (which appears impossible under the pinching/broadcasting-Hamiltonian assumption) or reframe the paper as a negative/limitation result, which is a substantial revision. The EWFS part (separable states, modified LF bound 2+4ε) is sound and could support a shorter paper. I would not recommend rejection outright, as the negative results are valuable, but the current version overstates its findings."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things worth knowing. The EWFS part is solid: broadcasting Hamiltonians force a separable post-measurement Lab state, so no LF-violating correlations survive, and the modified bound <CHSH> <= 2+4ε for imperfect 'asking the Friend' measurements is a clean, citable result. The WF-QD part, however, overclaims: the Δ≫ε signature in Fig. 4 does not establish a genuine Wigner's Friend effect, and the stress-test note explains why. ε in Eq. (20) is not a state-discrimination error. With p0=p1 it is ½|e0−e1|, so it vanishes for symmetric noise even when Wigner misreads the Friend 20% of the time. The M_L POVM in Eq. (A6) is a classical parity check on Helstrom outcomes. Because the pinching map deletes all inter-branch coherence in Eq. (17), the state is a separable mixture over the pointer outcome i; Δ is just the probability that two noisy classical channels disagree. The Friend's SBS assignment in Eq. (18) is built from the same Helstrom projectors used to define Wigner's measurement, so the comparison partly measures how far the noisy channels are from perfect noiseless ones. That is model misspecification, not a quantum effect. The Sec. IV claim that Wigner exploits 'coherence between the Friend and the environment' is hard to support given Eq. (17) contains no such coherence terms.\n\nCredit where due: the error taxonomy in Table II is genuinely useful; the numerical model is transparent and the authors are honest about the p0=0.75 case in Appendix C, where the claimed effect does not survive; and the EWFS bound is derived cleanly. The citation pattern looks fair, building on [13,14] and comparing with Relaño's decoherence treatment. No code or data files are shipped, but the numerical recipe is simple enough to re-implement.\n\nThe paper deserves a serious referee. The central simple-WF claim is not sound, but the framework, the taxonomy, and the EWFS result are worth engaging, and the specific flaw is instructive. I would not cite the WF-QD demonstration as evidence for a genuine WF effect, but I would cite the modified LF bound. Bring it to a reading group if you want a concrete example of why a decoherence model can look like it produces Wigner's Friend effects when it is only producing classical state-discrimination errors.","headline":"The EWFS/LF bound is solid and worth taking seriously; the headline 'genuine WF effect' in the simple QD model is a classical state-discrimination artifact, not a quantum effect.","tokens_in":26819,"tokens_out":6739,"would_cite":true,"duration_ms":77621,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Wigner–Friend-type disagreements can survive a decohering environment when the Friend and the environment are made of multiple qubits.","keywords":["Wigner's Friend","quantum Darwinism","decoherence","objectivity","local friendliness","state discrimination","spectrum broadcast structure","emergence of classicality"],"falsifier":"Simulate the WF-QD model with the Friend's assignment computed from optimal discrimination projectors evaluated on states averaged over many random Hamiltonian samples (or on a reduced description that omits the environment), instead of the actual conditional states of a single run; if the resulting disagreement $\\Delta$ falls to the level of $\\epsilon$, the reported Wigner–Friend effect is an artifact of the Friend's unrealistic perfect knowledge.","tokens_in":2028,"feed_emoji":"⚛️","tokens_out":5705,"duration_ms":147905,"temperature":0.7,"pith_summary":"This paper asks whether Wigner's Friend paradox survives when the Friend's measurement is modelled as a decohering quantum-Darwinism process rather than as a single-qubit idealization. It constructs a simple Wigner's Friend scenario in which the Lab contains a system, a Friend made of multiple qubits, and an environment made of multiple qubits, with the measurement generated by a broadcasting Hamiltonian and a pinching map. The paper reports that for equal pointer probabilities, a whole-Lab measurement produces a disagreement between Wigner's and the Friend's probability assignments of roughly 0.3 to 0.4, while the unavoidable state-discrimination error is between $10^{-5}$ and 0.012, so the disagreement clearly exceeds the error threshold. It also extends the model to extended Wigner's Friend scenarios and finds that broadcasting Hamiltonians make Local Friendliness violations impossible, and that the model's non-objectivity tightens the effective LF inequality. The interest is that genuine Wigner–Friend-type effects can coexist with a decohering environment and fade only as the Friend grows, which is a concrete step toward studying the emergence of classicality.","feed_headline":"Wigner–Friend effect survives decoherence in multi-qubit model","feed_subtitle":"A multi-qubit simulation finds Wigner's predictions differing from the Friend's by up to 0.4, far above the readout error.","key_machinery":"The machinery is a broadcasting Hamiltonian—a pointer-basis projector on the system coupled to conditional Hamiltonians on every qubit of the Friend and environment—together with a pinching map that dephases the initial state in the Hamiltonian eigenbasis, producing an SBS-like Lab state $\\rho_L = \\sum_i p_i |i\\rangle\\langle i|_S \\otimes \\rho_F^{(i)} \\otimes \\rho_E^{(i)}$ with small non-objectivity. The Friend's optimal SBS assignment uses the optimal discrimination projectors $\\Pi_F^{(i)}$ and $\\Pi_E^{(i)}$ that optimally discriminate the conditional states; Wigner's candidate whole-Lab measurement $M^0_L/M^1_L$ is built from combinations of these projectors with pointer projectors on the system, and asks whether the Friend and environment indices agree. The argument proceeds by comparing the disagreement $\\Delta$ for this POVM with the state-discrimination error $\\epsilon$ for the i-basis measurement, declaring a genuine Wigner–Friend effect only when $\\Delta \\gg \\epsilon$.","core_discovery":"The central claim is that a Wigner–Friend effect—a disagreement in probability assignments between Wigner and his Friend that cannot be written off as measurement inaccuracy—survives in a quantum-Darwinism model of the Friend's measurement. In the WF-QD model the post-measurement Lab state is spectrum-broadcast-like rather than exactly a spectrum broadcast structure, so the Friend's optimal assignment, built from optimal discrimination projectors on her own macrofraction and on the environment, differs from Wigner's state. For the measurement $M^0_L$, which asks whether the Friend and the environment record the same outcome, the paper finds numerically that the disagreement parameter $\\Delta$ lies between roughly 0.3 and 0.4 while the state-discrimination error $\\epsilon$ lies between $10^{-5}$ and 0.012, so $\\Delta \\gg \\epsilon$. The paper therefore claims to have satisfied the goal of observing Wigner's Friend effects in this model, identifies the effect as a novel form that exploits coherence between the Friend and the environment, and reports hints that the effect decreases as the Friend grows, signalling the emergence of classicality.","pith_inferences":["A natural extension is to replace the Friend's ideal assignment (built from the exact conditional states of her macrofraction and the environment) with a coarse-grained or averaged description; the paper's own 'Bad Friend' comparison suggests that any realistic lack of such knowledge would shrink $\\Delta$, so the reported effect can be read as an upper bound on what a physically situated Friend co","The $\\epsilon \\ge 0.207$ threshold for LF violations suggests a concrete numerical search: for intermediate Friend sizes, the non-objectivity correction is small enough that violations might reappear if a non-broadcasting Hamiltonian supplies the $\\sigma$ terms needed for entanglement between Labs; the paper leaves this window open.","Because $M^0_L$ is essentially an objectivity check—it tests whether the Friend and environment record the same outcome—the WF effect here is tied to the same mechanism that produces consensus in quantum Darwinism; one could test whether any whole-Lab observable yields $\\Delta \\gg \\epsilon$, or whether $M^0_L$ is special."],"forward_implications":["If the WF-QD result is correct, Wigner–Friend-type disagreements are not an artifact of single-qubit idealisations; they can persist in a decohering Lab with a multi-qubit Friend and environment.","In the extended scenario, any measurement governed by a broadcasting Hamiltonian produces a separable post-measurement state of the two Labs, so Local Friendliness inequalities cannot be violated under that dynamics.","The model's non-objectivity loosens the LF inequality to $\\langle CHSH \\rangle \\le 2 + 4\\epsilon$, making violation impossible once $\\epsilon \\ge (\\sqrt{2}-1)/2 \\approx 0.207$; numerically, that threshold is exceeded for small Friends (2–4 qubits) and only crossed for larger ones.","Unequal pointer probabilities ($p_0 \\ne p_1$) erase the clear $\\Delta \\gg \\epsilon$ separation in the simple scenario, so the reported genuine WF effect is specific to the equal-probability case and the particular $M^0_L$ measurement.","The size-dependent decline of the effect in the equal-probability case hints that WF effects vanish in the thermodynamic limit, marking the emergence of classicality as the Friend grows."],"supporting_citations":[{"why":"It supplies the no-go theorem for observer-independent facts used as the reference point for extended Wigner's Friend scenarios.","marker":"[3]"},{"why":"It states the local friendliness assumptions and the CHSH-like inequality against which the EWFS-QD results are benchmarked.","marker":"[5]"},{"why":"It provides the decoherence framework for Wigner's Friend experiments that this work extends and compares against for the environment case.","marker":"[9]"},{"why":"It introduces the unitary equilibration model of measurement that motivates modelling the Friend's measurement as a broadcasting Hamiltonian process.","marker":"[13]"},{"why":"It supplies the pinching-map prescription and the optimal projectors used for the Friend's SBS assignment and for Wigner's measurements.","marker":"[14]"},{"why":"It proves that strong quantum Darwinism plus strong independence is equivalent to spectrum broadcast structure, grounding the SBS-like state assumption.","marker":"[34]"},{"why":"It derives the modified local friendliness inequalities with the epsilon correction used to bound LF violations in the EWFS-QD model.","marker":"[45]"},{"why":"It provides the formalism for optimal two-outcome quantum state discrimination used to define Wigner's optimal measurement and the error parameter.","marker":"[46]"}],"fun_headline_variants":["Quantum Darwinism tests Wigner's Friend, effect persists","Wigner's Friend effect endures in noisy quantum model","Novel Wigner-Friend effect emerges despite decoherence","Classicality emerges as Wigner's Friend effect fades"],"cache_read_input_tokens":28800,"weakest_assumption_plain":"The load-bearing premise is that the Friend can build her best post-measurement state from projectors that perfectly distinguish the exact conditional states of her own qubits and of the inaccessible environment; without that detailed knowledge her assignment would differ, and the large disagreement reported for the whole-Lab measurement (built from the same projectors) would not be a fair measure of the Wigner–Friend effect.","fun_headline_variants_meta":{"raw":{"variants":["Quantum Darwinism tests Wigner's Friend, effect persists","Wigner's Friend effect endures in noisy quantum model","Novel Wigner-Friend effect emerges despite decoherence","Classicality emerges as Wigner's Friend effect fades"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000661,"raw_usage":{"total_tokens":3072,"prompt_tokens":1044,"completion_tokens":2028,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":660,"completion_tokens_details":{"reasoning_tokens":1959}},"tokens_in":660,"tokens_out":2028,"duration_ms":17348,"temperature":1.0,"reasoning_tokens":1959,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T13:00:06.733188+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate the WF-QD model with the Friend's assignment computed from optimal discrimination projectors evaluated on states averaged over many random Hamiltonian samples (or on a reduced description that omits the environment), instead of the actual conditional states of a single run; if the resulting disagreement $\\Delta$ falls to the level of $\\epsilon$, the reported Wigner–Friend effect is an artifact of the Friend's unrealistic perfect knowledge.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It supplies the no-go theorem for observer-independent facts used as the reference point for extended Wigner's Friend scenarios."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It states the local friendliness assumptions and the CHSH-like inequality against which the EWFS-QD results are benchmarked."},{"cited_title":"A strong no-go theorem on the wigner’s friend paradox","cited_arxiv_id":null,"evidence_quote":"It introduces the unitary equilibration model of measurement that motivates modelling the Friend's measurement as a broadcasting Hamiltonian process."},{"cited_title":"Experimental test of local observer independence","cited_arxiv_id":null,"evidence_quote":"It supplies the pinching-map prescription and the optimal projectors used for the Friend's SBS assignment and for Wigner's measurements."},{"cited_title":"Quantum mechanical evo- lution towards thermal equilibrium.Physical Re- view E , 79(6):061103, 2009","cited_arxiv_id":null,"evidence_quote":"It derives the modified local friendliness inequalities with the epsilon correction used to bound LF violations in the EWFS-QD model."},{"cited_title":"Equilibration of quantum sys- tems and subsystems","cited_arxiv_id":null,"evidence_quote":"It provides the formalism for optimal two-outcome quantum state discrimination used to define Wigner's optimal measurement and the error parameter."}],"review_version":1}