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arxiv: 2309.13826 · v2 · submitted 2023-09-25 · 🪐 quant-ph

Quantum Superpositions of Conscious States in a Minimal Integrated Information Model

Kelvin J. McQueen , Ian T. Durham , Markus P. Mueller This is my paper

Pith reviewed 2026-05-24 06:45 UTC · model grok-4.3

classification 🪐 quant-ph
keywords integrated information theoryquantum consciousnesswave function collapseLindblad master equationWigner's friend experimentsuperposition of conscious states
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The pith

A minimal quantum model of superposed conscious states forces proliferation of collapse operators in Lindblad dynamics.

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

The authors construct a feedback dyad in a quantum circuit that enters a superposition of states with different integrated information values. They demonstrate that standard collapse dynamics of Lindblad type cannot have rates depend solely on the qualitative differences between these conscious states if only a small number of operators are used. Instead, many commuting operators must be introduced, leading to a rapid increase in the number of terms in the dynamics. This complexity directly challenges the experimental tractability of IIT-based collapse models and similar Wigner-style theories.

Core claim

We construct a Schrödinger's dyad that places a minimal system into a superposition of states differing in their conscious structures according to integrated information theory. We prove that for Lindblad collapse to depend on qualitative differences in these states, many commuting collapse operators are required, causing a proliferation of terms even in this simple case.

What carries the argument

The structural constraint on Lindblad collapse dynamics that limits the dependence of rates on conscious state differences when few collapse operators are available.

If this is right

  • Collapse rates cannot in general be made to depend solely on qualitative differences with too few operators.
  • The required dynamics for IIT-based collapse becomes highly complex even for very simple systems.
  • Any theory distinguishing experiences using rich internal organization will face comparable explosion in dynamical complexity.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The direct mapping from IIT structures to collapse operators may not hold without further physical assumptions.
  • This proliferation could make experimental tests of such models more difficult than previously thought.
  • The issue is general to any consciousness theory relying on detailed internal structure rather than just quantitative measures.

Load-bearing premise

The conscious states are fully characterized by their IIT phi-values and associated structures that map directly onto distinct collapse operators.

What would settle it

Finding a set of few collapse operators in the Lindblad equation for the dyad that produces rates depending only on the qualitative IIT differences would falsify the proven constraint.

Figures

Figures reproduced from arXiv: 2309.13826 by Ian T. Durham, Kelvin J. McQueen, Markus P. Mueller.

Figure 1
Figure 1. Figure 1: The logical SWAP gate simply exchanges the values [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The SWAP gate considered as a feedback system over a [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: A possible implementation of the dyad. The dashed l [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗
Figure 3
Figure 3. Figure 3: Whereas channels [PITH_FULL_IMAGE:figures/full_fig_p030_3.png] view at source ↗
read the original abstract

Could there be quantum superpositions of conscious states, as suggested by the Wigner's friend thought experiment? Mathematical theories of consciousness, notably Integrated Information Theory (IIT), make this question more precise by associating physical systems with both quantitative amounts of consciousness and structural characterizations of conscious states. Motivated by a recent proposal that ties wave function collapse to integrated information, we construct a simple quantum circuit that would place a minimal system -- a feedback dyad -- into a superposition of states that differ in their associated conscious states. This "Schr\"odinger's dyad" provides a controlled setting for evaluating a central desideratum of consciousness-based collapse models: that collapse rates depend on how different the experiences in the superposition are. We prove a structural constraint on collapse dynamics of a standard (Lindblad) type: if collapse is governed by too few collapse operators, collapse rates cannot in general be made to depend solely on qualitative differences between conscious states. Avoiding this limitation requires introducing many commuting operators, leading to a rapid proliferation of collapse terms even for very simple systems. This proliferation bears directly on claims that IIT-based collapse theories may be especially experimentally tractable, since the required dynamics becomes highly complex. More generally, the difficulty is not specific to IIT: any Wigner-style collapse theory that distinguishes experiences using rich internal organization (such as neural connectivity in addition to neural state) will face a comparable explosion in dynamical complexity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper constructs a minimal quantum circuit ('Schrödinger's dyad') placing a feedback system into superposition of states distinguished by their IIT phi-values and structures. It proves a structural constraint on Lindblad-type collapse: with too few collapse operators, rates cannot in general be made to depend solely on qualitative differences between conscious states. Avoiding the limitation requires many commuting operators, producing rapid proliferation of terms even for simple systems. This bears on experimental tractability claims for IIT-based collapse models and generalizes to any Wigner-style theory using rich internal organization to distinguish experiences.

Significance. If the central constraint holds, the work identifies a concrete dynamical-complexity barrier for consciousness-based collapse models that tie rates to qualitative experience differences via IIT (or analogous rich structures). The derivation supplies a mathematical, parameter-free result from the Lindblad form and state distinctions, which is a strength. It directly challenges tractability arguments without relying on fitted parameters or self-reference.

major comments (1)
  1. [Schrödinger's dyad construction] Schrödinger's dyad construction (abstract and construction paragraph): the claimed injection from distinct IIT phi-structures (including internal organization) into the space of collapse operators is treated as given once phi-values differ, but no explicit rule is supplied showing that operator commutators or supports follow from the IIT axioms alone. This mapping is load-bearing for the structural constraint; without it the result applies only under additional physical postulates (e.g., preferred basis).

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and the identification of an important point of clarification regarding the Schrödinger's dyad construction. We address the major comment below.

read point-by-point responses

  1. Referee: Schrödinger's dyad construction (abstract and construction paragraph): the claimed injection from distinct IIT phi-structures (including internal organization) into the space of collapse operators is treated as given once phi-values differ, but no explicit rule is supplied showing that operator commutators or supports follow from the IIT axioms alone. This mapping is load-bearing for the structural constraint; without it the result applies only under additional physical postulates (e.g., preferred basis).

    Authors: We agree that the manuscript does not derive an explicit mapping from the IIT axioms to the commutators or supports of collapse operators. The paper instead starts from the modeling assumption that collapse rates in an IIT-based theory are to depend on the qualitative differences between conscious states (as characterized by both phi-value and structure). Under this assumption, the Lindblad form cannot achieve rate dependence solely on those differences unless the operators are chosen to reflect the distinctions; with too few operators the rates necessarily retain dependence on the superposition basis itself. The structural constraint is therefore a general feature of the Lindblad equation when the target distinctions rely on rich internal organization, independent of any claim that IIT axioms alone fix the operator algebra. We will revise the abstract and construction paragraph to state this modeling assumption explicitly and to note that it constitutes an additional physical postulate (operator selection aligned with IIT-defined experiences). This clarification does not alter the central result but makes its scope precise. revision: partial

Circularity Check

0 steps flagged

No circularity: Lindblad constraint derived from operator algebra under explicit IIT mapping assumption

full rationale

The central result is a mathematical proof that too few Lindblad operators cannot make collapse rates depend solely on qualitative differences between IIT-characterized states. This follows directly from the Lindblad form and the modeling choice to associate distinct phi-structures with distinct operators; the proof does not reduce any quantity to a fitted input or self-referential definition. The mapping from IIT structures to collapse operators is stated as an assumption in the Schrödinger's dyad construction rather than derived within the paper, so no self-definitional loop exists. Motivation from a prior collapse-IIT proposal is cited but does not carry the load of the operator-counting argument. The derivation remains self-contained against the stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard quantum mechanics (Lindblad master equation), the assumption that IIT phi-structures distinguish conscious states in a way that can be coupled to collapse operators, and the modeling choice of a minimal feedback dyad. No free parameters are fitted; no new entities are postulated.

axioms (2)
  • domain assumption Conscious states are distinguished by their IIT-integrated information structures in addition to scalar phi values.
    Invoked when mapping superposed states to distinct collapse behaviors (abstract).
  • standard math Collapse dynamics are of Lindblad form with a finite set of operators.
    Explicitly used to derive the structural constraint on operator count.

pith-pipeline@v0.9.0 · 5785 in / 1394 out tokens · 19803 ms · 2026-05-24T06:45:28.632229+00:00 · methodology

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    |1⟩. We then partition the system as usual and calculate the integrated effect infor mation by evaluating the QID over the eigenstate for a particular partition such that φe = QID(ρ∥σ) = pi   log(pi) − ∑ j Pij log(qθ j )   (21) where σ = ∑ j qθ j |j⟩ ⟨j| is now the partitioned effect repertoire. We can then begin by identifying three subsystems as befor...

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    Equation 21 then reads in full φe(bt0 = ρ+) = pi   log(pi) − ∑ j Pij log(qθ j )   (24) = 1 · (0 + 1) = 1 . The calculation for φc is identical except the pi are for the present state and the qj are for the past state. For the case in which A’s present state is ρ0 we thus find that φc(at0 = ρ0) = 1 and, likewise for the case in which B’s present state i...

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