Decoherence framework for Wigner's friend experiments

Armando Rela\~no

REVIEW 3 major objections 4 minor 29 references

Decoherence framework for Wigner's friend experiments

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper claims that in Wigner-friend experiments an external interference measurement rewrites the inner agent's memory in a computable way, and that accounting for this change removes the known contradictions.

desk verdict A serious decoherence-based reply to Wigner's friend no-go theorems with a clean falsifiable prediction (S=1/√2), but the FR resolution rests on a conditioning slip that needs fixing. read the letter →

arxiv 1908.09737 v2 pith:JAQCAOG6 submitted 2019-08-26 quant-ph

Armando Relaño This is my paper · ORCID

classification quant-ph

keywords Wigner'sfrienddecoherencepointerstatesenvironment-inducedcollapseobserver-independentfactsCHSHinequalityquantummeasurementproblemmachines

topics The Measurement Problem

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 applies the decoherence interpretation of quantum measurements to Wigner-friend experiments, arguing that a definite outcome appears only after an uncontrolled environment with orthogonal branch states monitors the system, apparatus, and observer. Within this framework every step remains unitary, and the apparent collapse is what the observer sees after tracing out that environment. The central new consequence is that the external interference measurement changes the friend's memory record in a calculable way: for an initial 50/50 horizontal/vertical state and external angle $\theta=\pi/8$, the record becomes $1/4$ horizontal and $3/4$ vertical instead of $1/2$ each. Taking these changes into account, the extended two-laboratory no-go arguments no longer force contradictory claims, and the modified four-agent CHSH test gives $S=1/\sqrt{2}$, compatible with joint truth values for all agents' outcomes. The paper explicitly leaves open whether the no-go theorems fail in general, treating their main statements as conjectures outside this framework.

What carries the argument

The load-bearing object is the environment: a set of qubits continuously coupled to the measuring apparatus through a chaotic interaction Hamiltonian. Its two pointer-branch states become orthogonal, $|\langle\varepsilon_1(t)|\varepsilon_2(t)\rangle|^2\sim 0$, which fixes the preferred basis and makes the global state's triorthogonal decomposition unique. Tracing out this environment converts the superposition into the mixed state the agent experiences, and tracing it out again after an external interference measurement produces the altered memory record of Eq. (26). The framework also depends on an exactly known apparatus-environment Hamiltonian, a known environmental initial state, and precisely timed external measurements.

What would settle it

Run the paper's three-stage protocol with roughly ten environment qubits per laboratory, an initial 50/50 horizontal/vertical state, and the external pre-measurement at $\theta=\pi/8$, making the external pre-measurement faster than the internal environment's correlation time. If the central claim is right, reading the friend's memory after the external interference over many runs gives horizontal with probability $1/4$ and vertical with $3/4$; finding the pre-interference $1/2$/$1/2$ statistics would falsify the framework.

Watch

Extended reading notes

Core claim

The central claim is that the decoherence interpretation supplies a univocal protocol for Wigner-friend experiments: after a measurement the real global state is an entangled superposition of the system, the apparatus, and an environment whose two branch states are orthogonal, and the observer's definite outcome is the mixed state obtained by tracing out that environment. Because the external agent's interference acts on the whole laboratory, it also changes the pointer-state probabilities that constitute the inner agent's memory. Equation (26) gives the new record for the standard one-photon case: tracing out the inner environment and the external apparatus and environment leaves $C_{hh}=(2-\sin 4\theta)/4$ and $C_{vv}=(2+\sin 4\theta)/4$, so at $\theta=\pi/8$ the friend's remembered statistics change from $1/2$/$1/2$ to $1/4$/$3/4$. Applying the same accounting to the extended two-laboratory protocol replaces the certainty of the original 'fact 1' with a probability split of $5/6$ versus $1/6$, thereby blocking the no-go conclusion. In the observer-independent-facts setup, the original version is said not to produce well-defined outcomes under this framework at all, while the modified version yields $S=1/\sqrt{2}<2$, allowing joint truth values for the four agents' memories.

Load-bearing premise

Everything rests on the postulate that a measurement is only complete when an uncontrollable environment, with two exactly orthogonal branch states, monitors the system-apparatus-observer composite; if that postulate fails, the predicted memory changes and the disappearance of the paradoxes do not follow.

Editorial extensions

If this is right

The friend's memory record is dynamical: an outside interference measurement at angle $\theta$ changes the recorded outcome distribution from $1/2$/$1/2$ to $(2-\sin 4\theta)/4$ versus $(2+\sin 4\theta)/4$, so identical machines in identical runs can honestly report different memories depending on when the memory is read.
The original extended no-go reasoning fails: conditioned on the internal agent's vertical outcome, the final external measurement yields $+_B$ not with certainty but with probability $5/6$, and $-A$ no longer implies $+_B$, so the joint outcome with probability $1/12$ is not ruled out.
The original observer-independent-facts test does not engage the decoherence framework because its initial state is only a pre-measurement; no definite outcomes exist until the environments act, so the CHSH violation concerns correlations of laboratory states, not observer facts.
In the modified four-agent protocol, applying CHSH to the final memory records gives $S=1/\sqrt{2}$, below 2, so joint truth values for all four agents' outcomes are consistent with the framework.
Wigner-friend interference on large, human-scale laboratories becomes practically impossible: the external pre-measurement must be completed faster than the internal environment's correlation time, so only small quantum machines can implement the experiment.

Reading between the lines

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

If this framework is right, the 'measurement problem' shifts partly into engineering: what counts as definite is determined by how many environment qubits each agent carries, so a few-qubit quantum machine with roughly ten environment qubits should already exhibit all Wigner-friend effects without any conscious observer.
The $1:3$ memory shift is a sharp discriminator: a real-collapse theory would leave the friend's record at $1:1$ after later interference, so an ensemble experiment comparing memory-read statistics before and after the external measurement could distinguish the two approaches.
A direct experimental next step would be to map the full $\sin 4\theta$ curve of Eq. (26) across many angles; a mismatch would immediately identify where the model's assumptions fail.
The requirement of a chaotic apparatus-environment interaction suggests that integrable environmental couplings will not produce definite outcomes; testing this with engineered non-chaotic environments could isolate the role of chaos in measurement.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things to know. First, the modified Brukner-style test is the real contribution: the authors construct a protocol where the four agents' memory records satisfy S=1/√2, a concrete and falsifiable prediction. The calculation is straightforward and appears correct. Second, the memory-change result in Eq. (26) — an external interference measurement shifts the friend's record from 1/2–1/2 to 1/4–3/4 — is clean and new. Those two pieces are worth keeping.

The paper is honest about its interpretational starting point: the decoherence postulate is stated plainly, and the authors admit that real-collapse theories would give different predictions. The numerics with GOE environments are a nice illustration, though the claim that a chaotic interaction is necessary is supported only by finite-size simulation; the paper itself flags this as a conjecture.

The soft spot is the Frauchiger-Renner section. The authors replace Fact 1 with “New fact 1” based on ρ3 in Eq. (49). But that ρ3 is obtained after tracing out EA's apparatus and environment, so the conditioning variable is IA's memory record after EA's interference — not the original v_a that appears in the FR chain. In the original v_a branch, the B state before EB is |+⟩_B, and EA's unitary acts only on A, so EB still sees + with certainty. The 5/6–1/6 split is a different conditional probability, mixing branches via the trace. As written, the paper does not establish that the FR contradiction disappears. This is a load-bearing flaw, not a typo.

Also, the inference from S<2 to joint assignability of truth values needs Fine's theorem or an explicit local model; the paper just asserts it. The abstract overstates “rules out all inconsistencies” relative to the careful limitations in Sec. VI.

Who benefits: people working on Wigner's friend experiments, decoherence, and the foundations of measurement. The Brukner modification and Eq. (26) are worth citing; the FR argument needs rethinking, not just polishing. I would send it to peer review with a referee who will press on the conditioning issue, because the paper has enough substance to justify referee time even if the final version looks quite different.

Referee Report

3 major / 4 minor

Summary. The paper develops a decoherence-based framework in which a quantum measurement is not completed until an uncontrolled environment, with exactly orthogonal branch states, monitors the system-apparatus-observer composite. It applies this framework to Wigner's friend experiments, deriving that an external interference measurement changes the internal agent's memory record in a calculable way (Eq. (26)), and it uses this effect to argue that the Frauchiger-Renner and Brukner no-go theorems are no longer valid. The paper also proposes a modified version of Brukner's experiment in which the final four-agent CHSH value becomes S=1/√2, and it supports the decoherence model with numerical simulations of a GOE environment.

Significance. The manuscript contains explicit, largely reproducible calculations: the reduced-state computation leading to Eq. (26), the four-agent state in Eq. (48), and the modified CHSH expectations in Eqs. (69)-(72). The S=1/√2 result is a parameter-free prediction of the modified protocol, and the numerical work on environment size and chaos is a concrete contribution to the decoherence-based modeling of Wigner's friend scenarios. If the framework's central postulate is accepted, the paper offers a coherent way to compute memory changes under external interference and gives predictions that differ from real-collapse models. However, the claimed resolution of the Frauchiger-Renner theorem is not established, because the argument replaces the conditioning event used in the original no-go chain with a different, later-time condition.

major comments (3)

[Sec. IV B, Eq. (49)] The replacement of 'Fact 1' by 'New fact 1' changes the conditioning variable. In the original Frauchiger-Renner chain, Fact 1 is a statement about the original outcome v_a obtained by IA before EA acts; it says that if IA obtains v_a, then a later measurement of laboratory B in the {|+>,|−>} basis will yield +_B. The calculation leading to Eq. (49) instead conditions on IA's memory record after EA's interference, with EA's outcome and apparatus traced out. These are different events: before EA acts, the original v_a branch has B=|+_B> as shown in Eq. (46), and since the EA unitary acts only on laboratory A, that branch's B component remains |+_B> until EB acts. If one further conditions on the h_B supplied by Fact 3a, the B state is |h_B>, so EB sees + or − with probability 1/2. The 5/6-1/6 split of Eq. (49) arises only after tracing over EA's outcome and apparatus, which mixes the original h_a and v_a branches into the same post-EA pointer state. Thus 'New fact 1' invalidates a different proposition from the one used in the no-go chain; the contradiction P(-A,-B)=1/12 versus P(-B|-A)=0 is not resolved by the calculation given.
[Sec. V B, Eqs. (69)-(72)] The conclusion that joint truth values can be assigned to all four agents' outcomes is inferred from the single value S=1/√2<2. For two-party, two-setting, two-outcome correlations, existence of a joint distribution for the four observables is guaranteed by Fine's theorem only when all CHSH inequalities (with all sign choices) hold, not by a single CHSH combination being below 2. The four expectation values computed here do satisfy all these inequalities, so the conclusion is likely correct, but the paper should invoke Fine's theorem explicitly; as written, the inference from one CHSH value to joint assignability is incomplete.
[Sec. II B and Table III] The framework's central postulate—that a measurement is completed only when an uncontrolled environment whose two branch states are exactly orthogonal monitors the system-apparatus-observer composite—is asserted and used as the basis for all later conclusions. The paper is transparent that its conclusions are conditional on this postulate, and it correctly notes that real-collapse theories would give different predictions. This is not an internal inconsistency, but it means the paper does not resolve the Frauchiger-Renner or Brukner paradoxes within quantum theory alone; it shows only that they do not arise under one particular extra postulate. The conclusions section should state this limitation more prominently, since the abstract's phrasing could be read as a stronger claim.

minor comments (4)

[Abstract and throughout] There are numerous typographical errors, including 'recenly', 'relizations', 'suposse', 'Copenhaguen', 'publised', 'objetivity', and 'diamons'. These should be corrected before publication.
[Sec. V A] The inequality in Eq. (63) is attributed to 'Claude-Horne-Shimony-Holt'; the correct name is Clauser-Horne-Shimony-Holt.
[Fig. 5 caption] The caption reads 'The number of qbits of both environment is N=6'; this should be 'both environments are N=6'.
[Sec. IV B, page 20] In the sentence introducing New Fact 1, 'the results are different is the decoherence framework is not taken into account' should read 'if the decoherence framework is not taken into account'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's claims are conditional consequences of an explicit decoherence postulate, and its quantitative results are analytic computations rather than fitted or self-citation-derived inputs.

full rationale

The paper is transparent that its framework rests on a postulate: a measurement is complete only when an uncontrolled environment with orthogonal branch states monitors the system-apparatus-observer composite (Eq. 8; facts F1/F2 in Table III). From that postulate, all central results are derived by explicit unitary evolution and partial tracing, not by fitting. The key quantitative prediction that external interference changes the internal agent's memory record, Eq. (26) with coefficients (1/4)(2−sin 4θ) and (1/4)(2+sin 4θ), is an analytic consequence of the stated Hamiltonian model, not a parameter fitted to the effect it is said to predict. Similarly, the modified Brukner-style protocol gives S=1/√2 by direct computation from the global state (Eq. 68) and the defined observables (Eqs. 65a–65d); no free parameter is adjusted to produce compatibility with joint truth values. The paper's relation to Frauchiger–Renner is also a computation: 'New fact 1' is obtained from the reduced state ρ3 (Eq. 49) after the external interference, and the paper explicitly warns that its conclusion differs from the standard interpretation. Whether this calculation correctly addresses the original no-go chain is a substantive correctness question about conditioning variables, not a circularity: the derivation does not presuppose the conclusion it draws. The self-citations present in the paper, Refs. [13] and [16] (Gómez et al., and Corps and Relaño), are used for standard random-matrix/chaos characterizations and are not load-bearing for the logical consistency claims; the uniqueness of the pointer basis is imported from the external Elby–Bub triorthogonal uniqueness theorem, not from the authors' own prior work. The paper also repeatedly disclaims that it has not disproved the no-go theorems in general, only that the specific examples fail under the decoherence framework. For all these reasons, no step reduces its predictions to its inputs by construction or by self-citation.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper's analytical results are derived from standard unitary quantum mechanics together with the decoherence postulate. No parameters are fitted to external data; the numerical model uses standard GOE random matrices and illustrative sizes and couplings. The central S=1/√2 result is parameter-free once the modified measurement protocol is fixed. The main burden is the decoherence postulate and the assumption that real environments are chaotic.

free parameters (4)

GOE coupling matrices Vh and Vv = not fitted; GOE with σ_diag=1, σ_off=1/√2
Model choices for the apparatus-environment interaction; the conclusion that decoherence occurs depends on these being chaotic, but the values are not fitted to data.
Environment size N (qbits) = not fitted; N=3 to 10 in figures
Illustrative sizes; the framework only requires N large enough that the environmental overlap decays to ~0. The specific N does not affect the central S=1/√2 derivation.
Coupling constant g = not fitted; g=1, 10, 100 in Fig. 7
Strength of the external pre-measurement; Eq. (26) is independent of g once g is large enough, and Fig. 7 shows small g fails.
Sparsity exponent α = not fitted; α=0, 0.5, 1, 2, 4
Controls the degree of chaos in the environment interaction. The paper argues that only α≤0.5 gives decoherence, so the framework's general validity is tied to this modeling assumption.

assumptions (5)

standard math Standard unitary quantum mechanics and the Born rule applied to reduced density matrices.
Used throughout to compute the perceptions of agents after tracing out environments.
domain assumption A measurement is completed only when an uncontrolled environment becomes correlated with system and apparatus and the environmental branch states become orthogonal (Eq. 8).
This is the defining postulate of the decoherence framework; the entire analysis is conditional on it.
domain assumption Agents are quantum machines with known Hamiltonians, and their memory records are the pointer states of the apparatus.
Stated in Sec. I to avoid modeling conscious beings; allows the memory states to be treated as part of the unitary evolution.
domain assumption The apparatus-environment interaction must be chaotic (GOE-like) for decoherence to occur.
Fig. 4 shows that integrable interactions (α≥2) do not suppress the environmental overlap; the paper treats chaotic behavior as necessary for the framework.
domain assumption External interference experiments can be performed on the complete laboratory including the environment, given requirements R1-R4 in Table II.
Required for the memory-change prediction of Eq. (26) to be testable; if this is physically impossible, the central prediction is moot.

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Pith. "Pith review of Decoherence framework for Wigner's friend experiments." pith.science (2026). https://pith.science/paper/JAQCAOG6

@misc{pith2026190809737,
  author       = {Pith},
  title        = {Pith review of: Decoherence framework for Wigner's friend experiments},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JAQCAOG6}},
  note         = {Machine review of arXiv:1908.09737}
}

read the original abstract

The decoherence interpretation of quantum measurements is applied to Wigner's friend experiments. A framework in which all the experimental outcomes arise from unitary evolutions is proposed. Within it, a measurement is not completed until an uncontrolled environment monitorizes the state composed by the system, the apparatus and the observer. The (apparent) wave-function collapse and the corresponding randomness result from tracing out this environment; it is thus the ultimate responsible for the emergence of definite outcomes. Two main effects arise from this fact. First, external interference measurements, trademark of Wigner's friend experiments, modify the memory records of the internal observers; this framework provides a univocal protocol to calculate all these changes. Second, it can be used to build a consistent scenario for the recenly proposed extended versions of the Wigner's friend experiment. Regarding [D. Frauchiger and R. Renner, {\em Quantum theory cannot consistently describe the use of itself}, Nat. Comm. {\bf 9}, 3711 (2018)], this framework shows that the agents' claims become consistent if the changes in their memories are properly taken into account. Furthermore, the particular setup discussed in [C. Brukner, {\em A no-go theorem for observer-indepdendent facts}, Entropy {\bf 20}, 350 (2018)] cannot be tested against the decoherence framework, because it does not give rise to well-defined outcomes according to this formalism. A variation of this setup, devised to fill this gap, makes it possible to assign joint truth values to the observations made by all the agents. This framework also narrows down the requisites for such experiments, making them virtually impossible to apply to conscious (human) beings. Notwithstanding, it also opens the door to future relizations on quantum machines.

Figures

Figures reproduced from arXiv: 1908.09737 by the authors.

**Figure 2.** FIG. 2. Panel (a), value of [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** FIG. 3. Ratio of consecutive level spacings distribution, [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: FIG. 4. Finite-size scaling for the long-time average of [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

**Figure 5.** Figure 5: FIG. 5. Panel (a), matrix elements [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]

**Figure 6.** Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]

**Figure 7.** Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

29 extracted references · 24 canonical work pages

[1]

E. P. Wigner, Remarks on the mind-body question . In The Scientiest Speculates, Ed. I. J. Good; Heinemann: London, UK (1961)

work page 1961
[2]

Following the same spirit, agent EB chooses between A1 and B1, A1 =|h⟩b|Ah⟩b⟨h|b⟨Ah|b−|v⟩b|Av⟩b⟨v|b⟨Av|b, (61) B1 =|+⟩B|+⟩B−|−⟩B⟨−|B, (62) where|±⟩B = (|h⟩b|Ah⟩b±|v⟩b|Av⟩b)/ √ 2

The ﬁrst one, A0, can be interpreted as a simple reading of agent’s IA memory, whereas the second one, B0, performs an external interference experiment, and therefore can be linked to agent’sEA memory. Following the same spirit, agent EB chooses between A1 and B1, A1 =|h⟩b|Ah⟩b⟨h|b⟨Ah|b−|v⟩b|Av⟩b⟨v|b⟨Av|b, (61) B1 =|+⟩B|+⟩B−|−⟩B⟨−|B, (62) where|±⟩B = (|h⟩...

work page
[3]

(63), applied to |Ψ4⟩ leads to S = 1/ √ 2< 2

(72) Therefore, the CHSH inequality, Eq. (63), applied to |Ψ4⟩ leads to S = 1/ √ 2< 2. Two main conclusions can be gathered from this section. First, the experiment devised in [3], and its experimental realization [4], are incompatible with the decoherence framework, because, according to it, they do not deal with proper outcomes; thus, they cannot be use...

work page
[4]

This means that we cannot assign joint truth values to the state of these laboratories, but we can make this assignement to the state of the agents memories. In [3, 4] there is no distinction between the state of the laboratory in which an agent lives, and the state of its memory; the decoherence framework is based precisely on this distinction. Before en...

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In other words, the environment, and its interaction with the measuring apparatus, is the origin of the classical perception of the reality

One of the trademarks of the decoherence interpretation of quantum mechanics is that the pointer states of any apparati, that is, the states which appear as objective outcomes, are those which survive to the continuous monitorization by a complex environment. In other words, t...
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Of course, the agent cannot restore the complete state from a single measurement. If its outcome is, say, h, it can just conclude that the global state must be |Ψ2⟩ =α|h⟩|Ah⟩|ϵ1(t)⟩ +β|v⟩|Av⟩|ϵ2(t)⟩, with unknown coeﬃcents α and β such that|α|2 +|β|2 = 1, and|α|> 0. It is very...
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From this point of view, we can consider that the measurement is done by a small quantum machine, and that an ampliﬁcation process is done by the environment afterwards. In this way, the pre-measurement can be considered purely quantum, whereas the ampliﬁcation, required for a...
[22]

An interesting question is what happens if the non-diagonal elements, Chv andCvh, are clearly diﬀerent from zero. In such a case, the interaction between the apparatus and the environment does not determine the pointer states of the apparatus, and therefore the agent cannot se...
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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

E. P. Wigner, Remarks on the mind-body question . In The Scientiest Speculates, Ed. I. J. Good; Heinemann: London, UK (1961)

work page 1961

[2] [2]

Following the same spirit, agent EB chooses between A1 and B1, A1 =|h⟩b|Ah⟩b⟨h|b⟨Ah|b−|v⟩b|Av⟩b⟨v|b⟨Av|b, (61) B1 =|+⟩B|+⟩B−|−⟩B⟨−|B, (62) where|±⟩B = (|h⟩b|Ah⟩b±|v⟩b|Av⟩b)/ √ 2

The ﬁrst one, A0, can be interpreted as a simple reading of agent’s IA memory, whereas the second one, B0, performs an external interference experiment, and therefore can be linked to agent’sEA memory. Following the same spirit, agent EB chooses between A1 and B1, A1 =|h⟩b|Ah⟩b⟨h|b⟨Ah|b−|v⟩b|Av⟩b⟨v|b⟨Av|b, (61) B1 =|+⟩B|+⟩B−|−⟩B⟨−|B, (62) where|±⟩B = (|h⟩...

work page

[3] [3]

(63), applied to |Ψ4⟩ leads to S = 1/ √ 2< 2

(72) Therefore, the CHSH inequality, Eq. (63), applied to |Ψ4⟩ leads to S = 1/ √ 2< 2. Two main conclusions can be gathered from this section. First, the experiment devised in [3], and its experimental realization [4], are incompatible with the decoherence framework, because, according to it, they do not deal with proper outcomes; thus, they cannot be use...

work page

[4] [4]

This means that we cannot assign joint truth values to the state of these laboratories, but we can make this assignement to the state of the agents memories. In [3, 4] there is no distinction between the state of the laboratory in which an agent lives, and the state of its memory; the decoherence framework is based precisely on this distinction. Before en...

work page

[5] [5]

Frauchiger and R

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