Measuring the integrated information of a quantum mechanism

Integrated information theory (IIT), originally a framework for characterizing consciousness through causal information, is extended to finite-dimensional quantum systems such as quantum logic gates. The authors translate a measure of intrinsic information into a density matrix formulation and adapt conditional independence to account for quantum entanglement. This quantum extension of IIT may reveal internal structure of composite quantum states and operators that standard information-theoretic analysis misses. The work aims to inform debates about the relationship 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 ($\varphi$) of a system subset to 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.