⚛️ quantum physics

Quantum Superpositions of Conscious States in a Minimal Integrated Information Model

This paper demonstrates that constructing a quantum circuit to test consciousness-based wave function collapse models, such as those derived from Integrated Information Theory, reveals a fundamental structural constraint where making collapse rates depend on the qualitative differences between conscious states necessitates an unmanageable proliferation of collapse operators, thereby challenging the experimental tractability of such theories.

Original authors: Kelvin J. McQueen, Ian T. Durham, Markus P. Mueller

Published 2026-04-09

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Kelvin J. McQueen, Ian T. Durham, Markus P. Mueller

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Question: Can a Cat Be Both Awake and Asleep?

Imagine the famous "Schrödinger's Cat" thought experiment. A cat is in a box, and according to quantum physics, it is in a superposition—meaning it is simultaneously alive and dead until someone looks.

But what if the cat isn't just alive or dead, but conscious? What if the cat is in a superposition of feeling happy and feeling sad at the same time?

This is the question the authors tackle. They ask: If consciousness is real, can two different conscious experiences exist in a quantum superposition? And if they do, does the universe "collapse" that superposition instantly, or does it take time?

The Tool: A "Consciousness Calculator" (IIT)

To answer this, the authors use a mathematical theory called Integrated Information Theory (IIT). Think of IIT as a "Consciousness Calculator."

The Old Way: You might think, "Is the system conscious? Yes/No."
The IIT Way: IIT gives a system a score (how much consciousness it has) and a shape (what that consciousness feels like).

The authors use a tiny, simple system called a "Feedback Dyad." Imagine two light switches, A and B, connected in a loop. If A is on, B turns off. If A is off, B turns on. They just swap states back and forth.

According to IIT, even this tiny system has a tiny bit of consciousness.
Crucially, the "shape" of the consciousness when the switches are (On, Off) is different from when they are (Off, On), even though the "amount" of consciousness is the same.

The Experiment: "Schrödinger's Dyad"

The authors propose a quantum circuit (a "Schrödinger's Dyad") where this tiny system is put into a superposition. It is simultaneously in the state (On, Off) and (Off, On).

In the language of the paper, this means the system is experiencing two different conscious realities at once.

The Conflict: The "Collapse" Dilemma

The paper investigates a specific idea: Consciousness causes the wave function to collapse.

The Rule: If two conscious experiences are very different (e.g., "I see red" vs. "I see blue"), the universe should force them to choose one reality very quickly. If they are similar, they can stay in a superposition longer.
The Goal: The authors wanted to see if we can build a simple mathematical model where the "speed of collapse" perfectly matches the "difference between experiences."

The Problem: The "One-Key" Lock

The authors tried to build this model using a single "collapse operator" (think of this as a single master key or a single dial that controls how fast things collapse).

They discovered a mathematical impossibility:

You cannot use one single dial to measure the distance between every possible pair of experiences.

The Analogy:
Imagine you have four cities: New York, London, Tokyo, and Sydney. You want to build a single "Distance Gauge" that tells you exactly how far apart any two cities are.

You set the gauge to measure the distance between NY and London.
But then, when you try to measure Tokyo and Sydney, the gauge gives you the wrong number because it's stuck on the NY-London setting.
To get the exact right distance for every pair of cities, you would need a separate gauge for every single pair.

In the paper, they prove that if you use only one collapse operator, you cannot make the collapse speed match the "qualitative difference" of the experiences. You will inevitably get it wrong for some pairs.

The Solution (and the Catch): The "Operator Explosion"

So, how do we fix it? We need more dials. We need a separate collapse operator for every single independent part of the "consciousness shape."

The Fix: If we add enough operators (dials), we can perfectly match the collapse speed to the difference in experiences.
The Catch: The number of dials needed grows explosively.

The Analogy:
For our tiny two-switch system, we might need a few dozen dials. But imagine a slightly larger system, like a small brain with just 5 neurons.

To track the "shape" of consciousness for that small brain, you would need 13,000+ dials.
For a slightly bigger brain, you would need millions.

The math shows that the "complexity" of the collapse mechanism explodes. It becomes so complicated that it's hard to imagine how nature could possibly run such a complex calculation just to decide when a wave function collapses.

Why Does This Matter?

It Challenges "Simple" Theories: Some scientists have suggested that consciousness-based collapse theories are simple and easy to test in the lab. This paper says, "Not so fast." To make the theory work correctly, the math becomes incredibly complex, even for tiny systems.
It's Not Just About IIT: The authors show this isn't just a flaw in IIT. Any theory that says "consciousness is defined by how parts of the brain are connected and talk to each other" (rather than just what they are doing right now) will face this same problem. The more complex the connections, the more "dials" you need to measure them.
The Counterfactual Trap: The core issue is that IIT defines consciousness based on what could happen (counterfactuals), not just what is happening. To measure the difference between two experiences, the universe has to calculate how the system would react to every possible change. That requires a massive amount of computational power (or in this case, a massive number of collapse operators).

The Bottom Line

The paper concludes that while it's theoretically possible to have a universe where consciousness causes quantum collapse, making that theory work requires a level of complexity that makes it very difficult to test or even believe is practical.

If the universe is collapsing wave functions based on the "shape" of our experiences, it's doing so with a mechanism that is far more complex and "expensive" than we previously thought. It's like trying to build a simple toy car, only to realize you need a factory the size of a city to manufacture the engine.

1. Problem Statement

The paper addresses a central question in the foundations of quantum mechanics and the philosophy of mind: Can conscious states exist in quantum superposition? This inquiry stems from the "Wigner's Friend" thought experiment, which suggests that if a conscious observer measures a quantum system, the observer themselves might enter a superposition of having experienced different outcomes.

While standard quantum mechanics allows for such superpositions, "consciousness-causes-collapse" theories (inspired by Wigner) propose that the act of consciousness triggers wave-function collapse. Recent proposals, specifically by Chalmers and McQueen, attempt to formalize this using Integrated Information Theory (IIT). These models suggest that the rate of wave-function collapse should depend on the qualitative difference between the conscious states in superposition:

Superpositions of very different experiences should collapse rapidly.
Superpositions of similar experiences should persist longer.

The authors investigate whether such a model is dynamically feasible and experimentally tractable. Specifically, they ask if a collapse model can be constructed where collapse rates depend solely on the qualitative differences between conscious states without introducing prohibitive dynamical complexity.

2. Methodology

The authors employ a rigorous mathematical approach combining quantum information theory, stochastic differential equations (Lindblad dynamics), and the formalism of Integrated Information Theory (IIT).

The Test System (Schrödinger's Dyad): They construct a minimal physical system called a "feedback dyad." This consists of two binary channels (A and B) connected by a logical SWAP gate in a feedback loop.
- Classically, the dyad has four states: $(0,0), (0,1), (1,0), (1,1)$ .
- According to IIT, these states possess a non-zero amount of integrated information ( $\Phi$ ), making them minimally conscious.
- Crucially, while all four states have the same $\Phi$ value, IIT (specifically the version used in the target proposal) assigns them distinct qualitative structures (called "Q-shapes" in IIT 3.0 or $\phi$ -structures in IIT 4.0).
Quantum Implementation: The authors propose a quantum circuit where the dyad is placed in a superposition of these distinct states (e.g., $|0,0\rangle + |1,0\rangle$ ).
Collapse Modeling: They analyze the dynamics of this system using a Lindblad-type collapse model. The goal is to determine if the collapse operator(s) can be tuned such that the decay rate of a superposition is a function only of the distance between the corresponding Q-shapes (qualitative differences).
Formal Analysis:
1. They first test a model with a single collapse operator.
2. They then analyze the requirements for a model with multiple commuting collapse operators.
3. They extend the analysis from IIT 3.0 (Q-shapes) to IIT 4.0 ( $\phi$ -structures) to ensure the results are not artifacts of a specific IIT version.

3. Key Contributions and Results

A. The "Single Operator" Impossibility Result

The authors prove a structural constraint on collapse models governed by too few operators.

The Constraint: If collapse is driven by a single operator (or a small number of operators), the collapse rates between pairs of states are determined by the Euclidean distances between the eigenvalues of that operator.
The Conflict: The qualitative distances between the dyad's four conscious states (Q-shapes) form a specific geometric structure (a tetrahedron in a high-dimensional space). It is mathematically impossible to map the eigenvalues of a single operator to these states such that the pairwise differences in eigenvalues perfectly match the pairwise qualitative distances of the Q-shapes.
Consequence: A single-operator model inevitably fails to track conscious differences accurately. It will either collapse "similar" states too quickly or "dissimilar" states too slowly, violating the core desideratum of the theory.

B. The "Operator Proliferation" Problem

To satisfy the requirement that collapse rates track qualitative differences, one must introduce a separate collapse operator for every independent component of the conscious structure.

The Cost: For the simple dyad, this requires a significant number of operators (e.g., 16 to 27 operators depending on the simplification).
Scaling: The complexity scales explosively with system size.
- In IIT 4.0, conscious states are defined by "relations" between distinctions. The number of relations grows combinatorially.
- Example: A 3-node system has ~60 relations; a 5-node system has >13,000 relations.
- A collapse model tracking these structures would require thousands of independent dynamical terms, rendering the model dynamically complex and experimentally intractable.

C. Robustness Across IIT Versions

The authors demonstrate that this difficulty is not specific to IIT 3.0 or the "Q-shape" formalism.

In IIT 4.0, conscious states are defined by $\phi$ -structures (distinctions and relations). Even though the dyad's $\phi$ -structure is identical across its four classical states (meaning IIT 4.0 might view them as the same experience), the underlying counterfactual causal structure (the Transition Probability Matrix) that defines the relations is complex.
Any theory that individuates experiences based on rich internal organization (connectivity, causal relations) rather than just instantaneous physical states will face the same operator proliferation. The need to track counterfactual causal dependencies forces the introduction of many independent collapse parameters.

4. Significance and Implications

Refutation of "Simple" Consciousness-Collapse Models: The paper challenges the claim that IIT-based consciousness-collapse models are simple or easily testable. The authors show that the requirement to make collapse rates depend on the structure of experience (rather than just physical mass or position) inevitably leads to a "proliferation of operators."
General Constraint on Wigner-Style Theories: The result suggests a general limitation for any theory where consciousness causes collapse. If experiences are defined by complex internal causal structures (as in IIT, and likely in most neurobiological theories), the collapse dynamics must be equally complex to distinguish between them.
Experimental Tractability: The extreme complexity of the required dynamics makes it difficult to distinguish "consciousness-induced collapse" from standard environmental decoherence. If nature implements a simplified version (e.g., using few operators), it would fail to track conscious differences accurately, undermining the theoretical motivation. If nature implements the full complex version, the model becomes too unwieldy to be a practical alternative to standard quantum mechanics.
Methodological Insight: The paper provides a concrete mathematical framework for testing consciousness-based collapse theories, moving the debate from philosophical speculation to dynamical constraints.

Conclusion

The paper concludes that while consciousness-based collapse models are not strictly ruled out, they face a severe dilemma:

Simplicity: Use few operators $\rightarrow$ Collapse rates fail to track qualitative differences between experiences (failing the theory's core premise).
Fidelity: Use many operators to track differences $\rightarrow$ The dynamics become exponentially complex and experimentally unmanageable.

This structural tension suggests that the idea of a simple, testable "consciousness causes collapse" mechanism is likely incompatible with the rich, counterfactual nature of conscious experience as described by Integrated Information Theory.