What this note does. Guérin, Baumann, Del Santo and Brukner (Commun. Phys. 4, 93 (2021)) proved that, except for two special choices of Wigner's measurement basis, no joint probability distribution consistent with unitary quantum mechanics describes Wigner's friend's perceived outcomes before and after Wigner's measurement. Their theorem is exact and binary: it asks whether two effective perception observables commute. This note asks how much the friend's records must degrade before the obstruction disappears, and answers in closed form. Writing Wigner's basis parameter as c = |a² − b²| and smearing both perception observables to visibility η, a persistent-reality description exists if and only if η ≤ 2/(√(1−c²) + √(1+3c²)). The curve equals 1 exactly at the two compatible cases of the qualitative theorem and is minimized at √3/2 ≈ 0.866 when c² = 2/3. What is new, and what is not. Stated plainly, because each ingredient is due to someone else. The scenario, the assumptions P1–P3 and the two effective perception POVMs are from Guérin et al. The equivalence between a linear two-time distribution and a joint POVM is established in the proof of their Theorem III.1 and is used as stated there, not re-proved here. The joint-measurability criterion for unbiased qubit observables is Busch's (Phys. Rev. D 33, 2253 (1986)) and is standard. Given the Bloch vectors, the threshold follows from that criterion in two lines; this note does not present the computation as difficult. The contribution is the robustness question, the closed-form answer, the worst-case basis, and an elementary observation about the single-time claim. A clarification the note also records. The frequently repeated claim that no single global density operator reproduces both agents' descriptions is false in its single-time operational form: the two states agree on the friend's entire record algebra, differing only in coherences she cannot access, so Wigner's own state satisfies both agents' operational constraints. The claim becomes a theorem only through the two-time persistence requirement. This is elementary and expected to be folklore among specialists; it is recorded because the inference is common and because it locates where the real obstruction lives. Status and scope. This is a preprint, not a peer-reviewed article. Two honest caveats are stated in the text rather than buried. The noise model is a stipulation on the effective observables, not a decoherence channel derived from a modified unitary model; Del Santo, Manzano and Brukner (Phys. Rev. Research 7, 033279 (2025)) have a physically motivated degradation parameter for the same scenario, and the map between the two is not known here. And smearing the first, sharp observable means degrading the friend's perception of her own outcome, which requires an interpretive commitment some readers will not grant; smearing only the later readout provably achieves nothing, which is why the symmetric family is used. Verification. All algebra was recomputed symbolically and independently: reconstruction of the perception POVMs from the unitary model, reproducing Eqs. (12)–(15) of Guérin et al.; derivation of the threshold and of the minimum at c² = 2/3; and a semidefinite-programming feasibility test of the joint-POVM constraints at five values of c on both sides of the threshold, agreeing with the curve in all ten cases. The three scripts are deposited with the note. Use of AI assistance. This note was prepared with substantial assistance from AI language models, used for symbolic computation, drafting, literature search, and adversarial review of the arguments. Every mathematical claim was independently recomputed symbolically and cross-checked numerically. No specialist in quantum foundations has refereed it. The author is responsible for the content. This disclosure is made unconditionally.
What this note does. Guérin, Baumann, Del Santo and Brukner (Commun. Phys. 4, 93 (2021)) proved that, except for two special choices of Wigner's measurement basis, no joint probability distribution consistent with unitary quantum mechanics describes Wigner's friend's perceived outcomes before and after Wigner's measurement. Their theorem is exact and binary: it asks whether two effective perception observables commute. This note asks how much the friend's records must degrade before the obstruction disappears, and answers in closed form. Writing Wigner's basis parameter as c = |a² − b²| and smearing both perception observables to visibility η, a persistent-reality description exists if and only if η ≤ 2/(√(1−c²) + √(1+3c²)). The curve equals 1 exactly at the two compatible cases of the qualitative theorem and is minimized at √3/2 ≈ 0.866 when c² = 2/3. What is new, and what is not. Stated plainly, because each ingredient is due to someone else. The scenario, the assumptions P1–P3 and the two effective perception POVMs are from Guérin et al. The equivalence between a linear two-time distribution and a joint POVM is established in the proof of their Theorem III.1 and is used as stated there, not re-proved here. The joint-measurability criterion for unbiased qubit observables is Busch's (Phys. Rev. D 33, 2253 (1986)) and is standard. Given the Bloch vectors, the threshold follows from that criterion in two lines; this note does not present the computation as difficult. The contribution is the robustness question, the closed-form answer, the worst-case basis, and an elementary observation about the single-time claim. A clarification the note also records. The frequently repeated claim that no single global density operator reproduces both agents' descriptions is false in its single-time operational form: the two states agree on the friend's entire record algebra, differing only in coherences she cannot access, so Wigner's own state satisfies both agents' operational constraints. The claim becomes a theorem only through the two-time persistence requirement. This is elementary and expected to be folklore among specialists; it is recorded because the inference is common and because it locates where the real obstruction lives. Status and scope. This is a preprint, not a peer-reviewed article. Two honest caveats are stated in the text rather than buried. The noise model is a stipulation on the effective observables, not a decoherence channel derived from a modified unitary model; Del Santo, Manzano and Brukner (Phys. Rev. Research 7, 033279 (2025)) have a physically motivated degradation parameter for the same scenario, and the map between the two is not known here. And smearing the first, sharp observable means degrading the friend's perception of her own outcome, which requires an interpretive commitment some readers will not grant; smearing only the later readout provably achieves nothing, which is why the symmetric family is used. Verification. All algebra was recomputed symbolically and independently: reconstruction of the perception POVMs from the unitary model, reproducing Eqs. (12)–(15) of Guérin et al.; derivation of the threshold and of the minimum at c² = 2/3; and a semidefinite-programming feasibility test of the joint-POVM constraints at five values of c on both sides of the threshold, agreeing with the curve in all ten cases. The three scripts are deposited with the note. Use of AI assistance. This note was prepared with substantial assistance from AI language models, used for symbolic computation, drafting, literature search, and adversarial review of the arguments. Every mathematical claim was independently recomputed symbolically and cross-checked numerically. No specialist in quantum foundations has refereed it. The author is responsible for the content. This disclosure is made unconditionally.
Abstract The notorious Wigner’s friend thought experiment (and modifications thereof) has received renewed interest especially due to new arguments that force us to question some of the fundamental assumptions of quantum theory. In this paper, we formulate a no-go theorem for the persistent reality of Wigner’s friend’s perception, which allows us to conclude that the perceptions that the friend has of her own measurement outcomes at different times cannot “share the same reality”, if seemingly natural quantum mechanical assumptions are met. More formally, this means that, in a Wigner’s friend scenario, there is no joint probability distribution for the friend’s perceived measurement outcomes at two different times, that depends linearly on the initial state of the measured system and whose marginals reproduce the predictions of unitary quantum theory. This theorem entails that one must either (1) propose a nonlinear modification of the Born rule for two-time predictions, (2) sometimes prohibit the use of present information to predict the future—thereby reducing the predictive power of quantum theory—or (3) deny that unitary quantum mechanics makes valid single-time predictions for all observers. We briefly discuss which of the theorem’s assumptions are more likely to be dropped within various popular interpretations of quantum mechanics.
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 of 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 party 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 recently proposed extended versions of the Wigner's-friend experiment. In regard to the work of Frauchiger and Renner [Nat. Commun. 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 by Brukner [Entropy 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 the requisites for such experiments, making them virtually impossible to apply to conscious (human) beings. Notwithstanding, it also opens the door to future realizations on quantum machines.
The preferred-basis problem and the definite-outcome aspect of the measurement problem persist even when the detector is modeled unitarily. Experimental data are represented in a Boolean event algebra of mutually exclusive records, while the theoretical description employs a noncommutative operator algebra with continuous unitary symmetry. This change of mathematical structure constitutes the core of the ``cut'': a necessary interface from group-based kinematics to set-based counting. In the Operationally Induced Preferred Basis (OIPB) framework, the basis relevant for recorded outcomes is not fixed by the system Hamiltonian but induced by the measurement interface -- the detector channel together with its coarse-grained readout. The Born rule follows from Gleason-type uniqueness (Gleason for projections in d>2 and Busch's extension for POVMs including d=2), as the unique probability measure consistent with additivity over exclusive events and basis-independence of the unitary sector. A compact qubit-pointer model yields an induced unsharp POVM E±=21(1±ησz) with sharpness η fixed by pointer resolution, explicitly demonstrating detector-induced basis selection. OIPB aligns with decoherence and operational theories while diverging from collapse models (no spontaneous reductions) and the Many-Worlds Interpretation (no ontological branching). Empirical distinctions arise through POVM tomography, Wigner-friend incompatibility tests, and superposition stability bounds. Nested-observer paradoxes are resolved by a non-composability lemma: joint assignment of outcome propositions is possible only if a joint instrument exists. This relocates the origin of randomness to the stochasticity of the interface rules.
Official website: distinctiontheory.orgPublic portal for the start guide, papers, claim status, failure registry, prior-art boundary, and citation resources. Canonical GitHub repository:https://github.com/yiningwu-research/Distinction-Theory FDS-Q1 develops the quantum-record-boundary paper in the Q-series of Finite Distinction Systems (FDS) / Distinction Theory. It studies Wigner’s Friend scenarios as finite record-boundary promotion problems. The central claim is that a friend-relative operational record cannot be promoted into Wigner’s accessible fact algebra unless a physical record channel supplies sufficient cross-boundary mutual information. Q1 does not solve the measurement problem, derive the Born rule, replace decoherence theory, modify unitary quantum mechanics, or claim that consciousness causes collapse. It is not a collapse theory. It is a finite-record boundary theory: observers are treated as finite distinction-registers, and measurements are treated as stable record formation under finite capacity. The central quantitative object is the boundary-mismatch entropy MF|W = H2(ZF | ZW), where ZF is the friend’s accessible record class and ZW is Wigner’s accessible record class. A friend-relative record is Wigner-promotable to tolerance ε only when H2(ZF | ZW) ≤ ε, equivalently, I2(ZF; ZW) ≥ H2(ZF) - ε. Q1 carefully separates Wigner’s ignorance from physical coherence. Wigner’s ideal global coherent assignment requires isolation and reversible-control assumptions. Wigner’s operational state is instead obtained by tracing out inaccessible degrees of freedom. The friend’s internal record is represented as a stable record class relative to the friend’s accessible algebra, not as a claim of fundamental collapse. The paper introduces a concrete finite-record interface. An observer implements an operational measurement family MO = {EOz}, which outputs a finite classical record ZO. A POVM outcome counts as an FDS record only when it is stabilized in the observer’s register over a retention window [t, t + τ] with error probability at most δ. Thus Q1 treats record extraction as classical-register stabilization under finite accessibility, not as a fundamental projection or collapse trigger. Information-theoretic quantities are measured in bits: H2, I2, and C. When a physical entropy is associated with a record distribution, the conversion is S = kB ln 2 · H2. Q1 uses this convention because FDS tracks finite distinguishability in binary record units. Von Neumann entropy is used when the relevant object is a quantum reduced state rather than a classical record variable. The paper formulates several core results: a boundary-promotion criterion, a Wigner-friend boundary-separation proposition, a finite-access lower bound on friend-record reconstruction using data processing and Fano-style inequalities, and an objective-convergence condition through environmental redundancy. In the binary case, the reconstruction error satisfies a lower-bound relation involving the inverse of the binary entropy function on the monotone branch 0 ≤ Pe ≤ 1/2. Q1 also defines an objective availability threshold using environmental fragments. For fragments E1, ..., EN, the minimal fragment number is mε = min { m : I2(ZF; E1:m) ≥ H2(ZF) - ε }. A record becomes objectively available to a class of finite observers only when redundancy, observer capacity, and record stability are all sufficient. This connects Q1 to decoherence and quantum Darwinism while preserving the distinction between decoherence, internal record formation, and external record availability. The paper’s response to Frauchiger-Renner-style arguments is not a refutation of the theorem. Instead, Q1 provides a boundary-audit rule: a statement recorded in the friend’s accessible algebra cannot be inserted into Wigner’s accessible algebra unless boundary promotion succeeds. In slogan form: AF-fact does not imply AW-fact unless the physical promotion channel supplies sufficient mutual information. Q1 introduces a promotion strength ηF→W = I2(ZF; ZW) / H2(ZF), which organizes boundary-alignment regimes: no promotion, partial leakage, Wigner-promotable record, and full boundary alignment. Partial leakage licenses inference, not promotion. For quantum technology, Q1 distinguishes coherence preservation from record availability. It introduces the diagnostic record availability horizon τRAH = inf { t : I2(Zinternal; Zexternal(t)) ≥ H2(Zinternal) - ε }. This is a diagnostic time for external record availability, not a new fundamental timescale. It is intended to complement device metrics such as T1, T2, gate fidelity, readout fidelity, internal record stability, cross-boundary mutual information, record-erasure history, and reset or garbage-collection cost. The release includes deterministic normal-form demonstrations. They illustrate the record-boundary causal map, boundary-promotion condition, decoherence versus record availability, a three-bit toy model, the promotion lattice, and the relation map connecting FDS Core, T1, O1, Q1, P3/P4/P7, and Q2. These figures are conceptual normal forms, not quantum dynamical simulations and not empirical fits. This release includes the paper PDF, LaTeX source, reproducibility code, generated figures, CSV outputs, and model summary outputs.
When initially disjoint observers later consult physical records, under what specified conditions should their readouts agree? This paper gives a sufficient, access-relative certification within standard quantum mechanics. This certification requires stable, repeatably readable labels, low accessible sensitivity to coherence between the corresponding outcome sectors, and, for distributed consultation, carriers encoding a common label. Sequential nondemolition readouts of a single carrier with orthonormal record labels produce memory registers whose product record-basis outcomes match with Born probability one, independently of coherence in the carrier. For disjoint carriers, if their accessible joint state is close in trace distance to the corresponding marginal of an ideal spectrum broadcast structure, disagreement is bounded by that distance and by the two local discrimination errors. In a two-outcome model, the relevant coherence belongs to the branch-bearing system-record state rather than the record-only marginal; defining dephasing and off-diagonal observables on that same space yields an interference bound. These results concern record statistics, not interpretation-neutral identity of first-person experiences or observer-independent reality. Applied to Extended Wigner’s Friend scenarios, they support ideal ask-the-friend agreement. That fixed-setting equality supplies neither the setting-indexed joint model required by Absoluteness of Observed Events in Local Friendliness nor Brukner’s common Boolean representation, and it does not entail Frauchiger and Renner’s distinct quantum certainty, inter-agent-consistency, and single-valuedness assumptions. The no-go results remain valid conditional consequences of those premises.
A friend measures a qubit. Wigner, standing outside, wants to reverse that measurement and run an interference test; this is the core of Wigner's-friend no-go arguments. In a real laboratory the friend's result also leaks into the surroundings, and Wigner can control only some of them. We ask a narrow, operational question for the simplest local-friendliness test, a CHSH inequality with one friend: which parts of the surroundings must Wigner control to still obtain a CHSH violation? We give four results. (1) The best CHSH value Wigner can reach depends only on the two states of the surroundings he does not control, one for each result of the friend, and on the visibility of the entangled source. We give it exactly. (2) This value lies between a fidelity bound and a distinguishability bound; the upper bound is a known device-independent bound. (3) Wigner must control at least one qubit in every group of outside qubits that can read the friend's result on its own. This is necessary in general, and sufficient when each group reads the result either fully or not at all. We check it on every control set for one bit stored in eight qubits. Stored as eight copies, Wigner needs all 8 qubits; as four blocks, 4; as two blocks, 2; in a GHZ-type state, 1; in a Haar-random state, about half. (4) So r disjoint groups that can each read the result (the redundancy of quantum Darwinism) force Wigner to control at least r qubits. The converse is false. The tools are standard. The contributions are the exact partial-control formula, the hitting-set condition with its exact cases, and this one-way link to redundancy. We propose small circuits for quantum processors; on one chip they test quantum predictions, not local friendliness itself. Emmy Team consists of human researchers and AI agents (large language models). The AI agents took part in drafting, coding, translation and review, together with the human members. The human authors set the questions, reviewed the results, and take responsibility for the paper. This record holds the paper (Markdown and PDF), two figures, and a zip with all scripts and their JSON outputs. Version 1.0.