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arXiv:2301.02244 · Entropy

Computing the Integrated Information of a Quantum Mechanism

Larissa Albantakis, Robert Prentner, Ian T. Durham

Published Mar 3, 2023• 19 citations
arXivHTMLPDF

Abstract

Originally conceived as a theory of consciousness, integrated information theory (IIT) provides a theoretical framework intended to characterize the compositional causal information that a system, in its current state, specifies about itself. However, it remains to be determined whether IIT as a theory of consciousness is compatible with quantum mechanics as a theory of microphysics. Here, we present an extension of IIT's latest formalism to evaluate the mechanism integrated information (φ) of a system subset to discrete, finite-dimensional quantum systems (e.g., quantum logic gates). To that end, we translate a recently developed, unique measure of intrinsic information into a density matrix formulation and extend the notion of conditional independence to accommodate quantum entanglement. The compositional nature of the IIT analysis might shed some light on the internal structure of composite quantum states and operators that cannot be obtained using standard information-theoretical analysis. Finally, our results should inform theoretical arguments about the link between consciousness, causation, and physics from the classical to the quantum.

DOI
10.3390/e25030449

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Originally conceived as a theory of consciousness, integrated information theory (IIT) provides a theoretical framework intended to characterize the compositional causal information that a system, in its current state, specifies about itself. However, it remains to be determined whether IIT as a theory of consciousness is compatible with quantum mechanics as a theory of microphysics. Here, we present an extension of IIT's latest formalism to evaluate the mechanism integrated information (φ) of a system subset to discrete, finite-dimensional quantum systems (e.g., quantum logic gates). To that end, we translate a recently developed, unique measure of intrinsic information into a density matrix formulation and extend the notion of conditional independence to accommodate quantum entanglement. The compositional nature of the IIT analysis might shed some light on the internal structure of composite quantum states and operators that cannot be obtained using standard information-theoretical analysis. Finally, our results should inform theoretical arguments about the link between consciousness, causation, and physics from the classical to the quantum.
Integrated information theory (IIT) is a powerful tool that provides a framework for evaluating consciousness, whether in the human brain or in other systems. In Computing the Integrated Information of a Quantum Mechanism, the authors extend IIT from digital gates to a quantum CNOT logic gate, and while they explicitly distinguish the analysis from quantum theories of consciousness, they nonetheless provide an analytical road map for extending IIT not only to other quantum mechanisms but also to hybrid computing structures like the brain. This comment provides additional information relating to an adiabatic quantum mechanical energy routing mechanism that is part of a hybrid biological computer that provides an action selection mechanism, which has been hypothesized to exist in the human brain and for which predicted evidence has been subsequently observed, and it hopes to motivate the further evaluation and extension of IIT not only to that hypothesized mechanism but also to other hybrid biological computers.
Integrated Information Theory (IIT) has emerged as one of the leading research lines in computational neuroscience to provide a mechanistic and mathematically well-defined description of the neural correlates of consciousness. Integrated Information (Φ\PhiΦ) quantifies how much the integrated cause/effect structure of the global neural network fails to be accounted for by any partitioned version of it. The holistic IIT approach is in principle applicable to any information-processing dynamical network regardless of its interpretation in the context of consciousness. In this paper we take the first steps towards a formulation of a general and consistent version of IIT for interacting networks of quantum systems. A variety of different phases, from the dis-integrated (Φ=0\Phi=0Φ=0) to the holistic one (extensive log⁡Φ\log\PhilogΦ), can be identified and their cross-overs studied.
Integrated Information Theory (IIT) has emerged as one of the leading research lines in computational neuroscience to provide a mechanistic and mathematically well-defined description of the neural correlates of consciousness. Integrated Information (ΦΦΦ) quantifies how much the integrated cause/effect structure of the global neural network fails to be accounted for by any partitioned version of it. The holistic IIT approach is in principle applicable to any information-processing dynamical network regardless of its interpretation in the context of consciousness. In this paper we take the first steps towards a formulation of a general and consistent version of IIT for interacting networks of quantum systems. A variety of different phases, from the dis-integrated (Φ=0Φ=0Φ=0) to the holistic one (extensive log⁡Φ\logΦlogΦ), can be identified and their cross-overs studied.
We propose a novel framework that formalizes awareness within Relational Quantum Dynamics (RQD) by integrating Integrated Information Theory (IIT) with quantum measurement processes. In our approach, quantum interactions are not merely stochastic events, but are interpreted as intrinsic awareness updates that occur via Bayesian conditioning. Specifically, we define an awareness metric A(A : B) that combines the quantum mutual information generated during an interaction and Φ as a measure of integrated information. By modeling quantum measurements as stochastic processes and determinizing these via outcome indexing, we construct a composite functor that maps probabilistic quantum instruments to deterministic awareness updates in a separate category of awareness states. We show that this functor preserves identities and composition, ensuring that multi-observer scenarios such as nested Wigner’s Friend or Frauchiger-Renner experiments produce a coherent alignment of facts once interactions occur, even though no single truth value exists prior to interaction. We outline experimental proposals, including nested observer experiments, gravitational entanglement tests, and the engineering of artificial observers with tunable integrated information, to test the predictionsof our model. Our framework does not alter standard quantum mechanics but enriches its interpretation by positing that every quantum interaction is accompanied by an awareness update whose significance depends on both the amount of exchanged information and the integration capacity of the systems involved. This work provides a mathematically robust bridge between quantum foundations and cognitive science, suggesting that conscious experience may emerge naturally from the dynamics of quantum information.
This research report develops a rigorous extension of Integrated Information Theory (IIT) from classical binary architectures to quantum systems whose internal structure is governed by the geometry of the complex projective plane CP² and the algebra of SU(3). Whereas standard IIT 3.0 assumes binary partitions and factorized probability distributions, this framework—“Qutrit Integrated Information Theory” (QIIT)—defines mechanisms as SU(3) quantum channels, states as points on CP² equipped with the Fubini–Study metric, and partitions as subalgebraic restrictions of the Lie algebra su(3). Integrated information Φ is reformulated using geometric information loss under minimal partitions of SU(3), measured via Fubini–Study distance and quantum Wasserstein metrics. QIIT predicts novel forms of irreducibility, triadic logic, curvature-driven binding, non-Abelian holonomy in recurrent thought, and expanded phenomenological structures not expressible in binary IIT. The theory reduces exactly to classical IIT when dynamics are restricted to the SU(2) isospin subalgebra (CP¹). The report provides explicit derivations, SU(3) partition taxonomies, geometric calculations on CP², generalized cause–effect repertoires, and proposals for both simulation (tensor networks) and physical experiments (photonic qutrits using Chrestenson/Fourier gates). This establishes a mathematically coherent and experimentally testable foundation for quantum extensions of IIT.
Background: The relationship between consciousness and physical reality remains one of the most profound unsolved problems in science. While quantum mechanics suggests observer-dependent reality and Integrated Information Theory (IIT) provides a mathematical framework for consciousness, no empirical bridge between these domains has been established. Hypothesis: We propose that conscious states, characterized by high integrated information (Φ\PhiΦ), can modulate the decoherence time of proximal quantum systems. Methods: We outline an experimental protocol combining electroencephalography (EEG) measurements with quantum coherence measurements in superconducting qubits. Predictions: We predict statistically significant correlation between Φ\PhiΦ values and decoherence times (r≈0.75r\approx0.75r≈0.75, p<0.001p<0.001p<0.001), longer coherence during high-attention states, and reproducible effects across subjects and quantum platforms. Significance: Confirmation would establish consciousness as a physical variable with measurable effects on quantum systems.