Computing the Integrated Information of a Quantum Mechanism.

Integrated information theory (IIT) was originally developed to characterize the causal information a system specifies about itself as a theory of consciousness, but its compatibility with quantum mechanics has been unclear. This work extends IIT's latest formalism to evaluate mechanism integrated information (φ) for discrete, finite-dimensional quantum systems such as quantum logic gates. The authors translate a measure of intrinsic information into a density matrix formulation and extend conditional independence to accommodate quantum entanglement. The compositional analysis may reveal structure in composite quantum states and operators not accessible through standard information-theoretical methods. The results aim to inform theoretical arguments about the links among consciousness, causation, and physics across classical and quantum domains.

Study at a glance

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.