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REVIEW 3 major objections 5 minor 68 references

Emergence of Classicality in Wigner's Friend Scenarios

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Wigner–Friend-type disagreements can survive a decohering environment when the Friend and the environment are made of multiple qubits.

desk verdict 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. read the letter →

arxiv 2507.21221 v1 pith:YMLLHG4T submitted 2025-07-28 quant-ph

Tom Rivlin , Sophie Engineer , Veronika Baumann This is my paper
classification quant-ph
keywords Wigner'sFriendquantumDarwinismdecoherenceobjectivitylocalfriendlinessstatediscriminationspectrumbroadcaststructureemergenceofclassicality
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks whether 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.

What carries the argument

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 $\Delta \gg \epsilon$.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

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

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

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.

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 (3)
  1. [Sec. II D, Eqs. (20) and (24)] 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.
  2. [Sec. II D, Eq. (A6)] 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.
  3. [Sec. II C, Eq. (18) and Appendix A 2] 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.
minor comments (5)
  1. [Sec. II C, Eq. (20)] 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)|.
  2. [Fig. 4 and Sec. II D] 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.
  3. [Sec. III B, Eq. (39)] 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.
  4. [Sec. II C, around Eq. (14)] 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.
  5. [Appendix A 2, Eq. (A6)] 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.

Circularity Check

2 steps flagged · score 6.0 of 10

The Δ≫ε WF-effect claim is built from the same Helstrom projectors on both sides: P_F(j=0)=1 is fixed by construction, Δ reduces to a classical parity error, and ε is only an asymmetry of Helstrom fidelities.

  1. self definitional [Sec. II C, Eq. (18); Appendix A 2, Eq. (A6), Fig. 4]
    "ρF_L = Σ_i p_i|i⟩⟨i|_S ⊗ Π(i)_F/Tr(Π(i)_F) ⊗ Π(i)_E/Tr(Π(i)_E), where the Π F and Π E represent the optimal effective description by the Friend of herself and her Lab’s environment [14, 40–43]. ... M 0_L = Π 0_S ⊗ Π 0_F ⊗ Π 0_E + Π 0_S ⊗ Π 1_F ⊗ Π 1_E + Π 1_S ⊗ Π 0_F ⊗ Π 0_E + Π 1_S ⊗ Π 1_F ⊗ Π 1_E."

    Inserting the Friend state (18) into Tr(M_L^0 ρ^F_L) gives p0·1 + p1·1 = 1 identically, because the POVM elements are products of the same Helstrom projectors used to define the Friend's assignment. Thus P^F(j=0)=1 is an identity, not a model prediction, and Δ = |1−P^W(j=0)| is exactly the probability that the Helstrom decisions on F and E disagree, i.e., a classical two-channel parity error. The Appendix A2 parenthetical only checks that Helstrom is optimal; it does not remove the double use of the same projectors on both sides of the WF comparison.

  2. self definitional [Sec. II D, Eqs. (20), (24)-(25), Fig. 4 caption]
    "If p0 = p1 = 0.5, this reduces down to P W (i = 0) = p0 (1 + e0 − e1), meaning that the ϵ parameter introduced in Eq. (20) is merely a function of e0 − e1. ... ∆ >> ϵ for all the NF and NE considered here signifies a genuine Wigner’s Friend effect."

    For p0=p1, Eq. (20) gives ε = 0.5|e0−e1|, so ε≈0 whenever the two Helstrom success probabilities are equal, even if both are poor (e.g., 0.8). The reported ε∈[1e−5,0.012] therefore only certifies e0≈e1, not that Wigner can read the Friend. Since Δ (previous step) is a parity error built from the same e_i, f_i, the inequality Δ≫ε is satisfied by symmetric classical readout noise. The criterion defining a 'genuine WF effect' is thus a self-referential comparison of two functions of the same Helstrom fidelities.

full rationale

The paper's QD simulations of non-objectivity versus NF (Fig. 3) and the EWFS modified-LF analysis are self-contained and not circular. The circularity is confined to the central WF-effect claim of Sec. II D: the Friend's SBS assignment (18) and Wigner's parity measurement (A6) are constructed from the same Helstrom projectors, forcing P_F(j=0)=1 and reducing Δ to a classical parity error. The paper briefly brackets a circularity worry in Appendix A2 but answers only the optimality of the POVM, not the shared-projector construction. Additionally, ε (Eq. 20) is not a total state-discrimination error for p0=p1; it is an asymmetry 0.5|e0−e1|, so the Δ≫ε test can pass for purely classical symmetric noise. Hence the headline 'genuine WF effect' is partially circular and definitional, while the size-dependence results and EWFS bounds retain independent content.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central numerical claims rest on the QD measurement model of [13,14] (pinching map, broadcasting Hamiltonians) plus a set of modeling choices: GUE sampling, all-qubits-in-|0> initial states, and the Friend's optimal-projector SBS assignment. No new physical entities are postulated. The main added structure is the classification of error sources (Table II) and the specific POVM M^0_L, neither of which is an independent ontological commitment.

assumptions (5)
  • domain assumption Pinching map as post-measurement state
    After the Friend's measurement, the Lab state is taken to be the pinching of the initial state under the broadcasting Hamiltonian (Eq. 16). This is borrowed from equilibration-on-average results [13,14,39] and is not derived here; all numerics depend on it.
  • domain assumption Broadcasting Hamiltonian without F-E coupling
    The Friend's measurement is modelled as unitary evolution under H_L = sum_i |i><i| x (H_F^(i) + H_E^(i)) with no direct interaction between Friend and environment (Eq. 15, Appendix A1). This restricts the model to states with no coherences between outcomes and no F-E coupling.
  • ad hoc to paper Friend's optimal SBS assignment uses true Helstrom projectors
    Equation (18) assigns the Friend the state built from Pi_F^(i), Pi_E^(i) obtained by optimal discrimination of the actual conditional states rho_F^(i), rho_E^(i). This presumes the Friend knows the very states she is supposed to lack access to (Sec. II C).
  • domain assumption Initial state with diagonal system and all environment qubits in |0>
    The system starts in a classical mixture p0|0><0|+p1|1><1| and all F/E qubits in |0> (Eqs. A2-A3). This is acknowledged as restrictive and non-natural (Appendix A1).
  • domain assumption GUE sampling for conditional Hamiltonians
    Each H_k^(i) is sampled from the Gaussian Unitary Ensemble to model generic chaotic dynamics (Appendix A1). Results are averages over 200 samples.

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Cite this review

Pith. "Pith review of Emergence of Classicality in Wigner's Friend Scenarios." pith.science (2026). https://pith.science/paper/YMLLHG4T

@misc{pith2026250721221,
  author       = {Pith},
  title        = {Pith review of: Emergence of Classicality in Wigner's Friend Scenarios},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YMLLHG4T}},
  note         = {Machine review of arXiv:2507.21221}
}
read the original abstract

The Wigner's Friend (WF) thought experiment concerns quantum measurements by a 'superobserver' of an observer measuring a quantum system. Variations on the setup and its extended versions have seen a resurgence in recent years, in light of a series of no-go theorems that reveal new quantum effects and question the existence of absolute events. But most theoretical and experimental studies of WF scenarios have restricted themselves to a 'friend' composed of a single qubit with idealised measurement settings in an idealised lab. In this work, we consider a specific, unitary model of the interaction between the Friend and the system in the presence of a decohering environment. In particular, we study WF scenarios from the perspective of quantum Darwinism (QD). The QD framework is well-suited to studying the questions of observations and agents in quantum theory that WF scenarios raise, as it is concerned with how observers record objective information about a system with access only to its surroundings. Here we describe how to add environments to simple and extended WF scenarios in the QD framework, and present numerical results that study the emergence of classicality, in the form of the Friend's measurement result becoming more objective. In both the simple and extended cases, we also find that the model and the environment obfuscate genuine WF effects and introduce strong restrictions on them. However, we also find a novel form of WF effect that exploits coherence between the Friend and the environment.

Figures

Figures reproduced from arXiv: 2507.21221 by the authors.

Figure 1
Figure 1. Left: In the simple Wigner’s Friend experiment of Sec. II A, the Friend (F) is situated in an isolated Lab (L) and performs a measurement on a quantum system S. Wigner (W) is outside of this Lab and performs a measurement on the whole Lab. Right: In the WF-QD setup of Sec. II C, an environment is added and the Friend is modelled as a collection of qubits. instead of the state ρ F L in Eq.(2). Note that |αii| 2 = P F… view at source ↗
Figure 2
Figure 2. Density plot of an SBS-like state of the whole Laboratory, [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Left: Plot (on a log scale) of a metric tracking the non-objectivity in the Friend, Tr ρ 0 F ρ 1 F  , as a function of NF , for different values of NE, when p0 = p1 = 0.5. 200 GUE samples were used to generate the points in these plots (the SEM is negligible and hence error bars are not plotted). The logarithmic best-fit line is intended solely to guide the eye. Right: A similar plot for the same scenario, but for … view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Left: Plot of Wigner’s measurement outcome P W (j = 0) when using the POVM with elements {M0 L , M1 L } (see Appendix A 2), against NF , for different values of NE, when p0 = p1 = 0.5. Plot generated using 200 GUE samples with negligible SEM. The best-fit lines are sol…
Figure 5
Figure 5. Figure 5: Extended Wigner’s Friend experiments: Subfigure [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]
Figure 6
Figure 6. Figure 6: Plot of ε (see Eq. (38)) against NC , for different values of NEC (with ND = NED = 1 for all points), for p0 = p1 = 0.5. The dashed line represents ε = √ 2 − 1  /2, the maximum value below which LF-inequality violations are possible. Plot generated using 200 GUE sampl…
Figure 7
Figure 7. Figure 7: Plot (on a log-scale) of the non-objectivity in the Friend, as measured by the overlap [PITH_FULL_IMAGE:figures/full_fig_p025_7.png]
Figure 8
Figure 8. Figure 8: Plot of the difference ∆ = |P W (j = 0) − P F (j = 0)| (solid data points), compared to the difference ϵ = |P W (i = 0) − P F (i = 0)| (hollow data points). ∆ and ϵ vary with NF , for different values of NE, when p0 = 0.75 and p1 = 0.25. Plot generated using 200 GUE sa…
Figure 9
Figure 9. Figure 9: Left: Plot of Wigner’s measurement outcome P W (j = 0) when using the POVM with elements {M0 L , M1 L } (see Appendix A 2), against NF , for different values of NE, when p0 = 0.75 and p1 = 0.25. Plot generated using 200 GUE samples. Unlike the other plots in this work,…

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Reference graph

Works this paper leans on

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    P (a, b|x, y) = P c,d P (a, b, c, d|x, y)

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  2. [2]

    P (a|c, d, x= 1 , y) = δac for all a, c, y ⇔ P (a = c|d, x= 1, y) = 1

    work page

  3. [3]

    P (b|c, d, x, y= 1) = δbd for all b, d, x ⇔ P (b = d|c, x, y= 1) = 1 • Local agency (LA) Freely chosen settings are uncorrelated with anything outside of their future light cone:

    work page

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    P (c, d|x, y) = P (c, d) (no super-determinism)

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    P (a|c, d, x, y) = P (a|c, d, x) (no-signaling)

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    P (b|c, d, x, y) = P (b|c, d, y) (no-signaling) In contrast to the simple Wigner’s Friend setup, we are now not concerned with how the two ‘Friends’ would model the post measurement state but rather whether measurements {Ax} and {By} by Alice and Bob can violate so-called Local Friendliness inequalities. They are derived from the LF assumptions analogous ...

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    As in the QD-E case of Sec

    This maximum violation occurs if, for ex- ample, A1 = 11 ⊗ |0⟩⟨0|C − 11 ⊗ |1⟩⟨1|C, A0 = |0, 0⟩ ⟨1, 1|LC − |1, 1⟩ ⟨0, 0|LC and analogously for B (see [3]). As in the QD-E case of Sec. II B, it is possible to describe a ‘EWFS-E’ case where a decohering environment is included inside Char- lie’s and Debbie’s Labs, EC and ED respectively. From the superobserv...

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    P (a = c|d, x= 1, y) ≥ 1 − ε 3′

    P (a, b|x, y) = P c,d P (a, b, c, d|x, y) 2′. P (a = c|d, x= 1, y) ≥ 1 − ε 3′. P (b = d|c, x, y= 1) ≥ 1 − ε, which leads to modified LF-inequalities. For the CSHS-like expression in Eq. (26), these read ⟨CHSH⟩ ≤2 + 4ε, (40) which means the larger the non-objectivity is (which in turn means larger values for ε), the harder it is for Alice and Bob to violat...

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.