Reply to Rourk, C. Comment on "Albantakis et al. Computing the Integrated Information of a Quantum Mechanism. Entropy 2023, 25, 449".

In response to a comment by Chris Rourk on our article Computing the Integrated Information of a Quantum Mechanism, we briefly (1) consider the role of potential hybrid/classical mechanisms from the perspective of integrated information theory (IIT), (2) discuss whether the (Q)IIT formalism needs to be extended to capture the hypothesized hybrid mechanism, and (3) clarify our motivation for developing a QIIT formalism and its scope of applicability.

Computing the Integrated Information of a Quantum Mechanism.

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.

A Formal Model for Adaptive Free Choice in Complex Systems.

In this article, I develop a formal model of free will for complex systems based on emergent properties and adaptive selection. The model is based on a process ontology in which a free choice is a singular process that takes a system from one macrostate to another. I quantify the model by introducing a formal measure of the 'freedom' of a singular choice. The 'free will' of a system, then, is emergent from the aggregate freedom of the choice processes carried out by the system. The focus in this model is on the actual choices themselves viewed in the context of processes. That is, the nature of the system making the choices is not considered. Nevertheless, my model does not necessarily conflict with models that are based on internal properties of the system. Rather it takes a behavioral approach by focusing on the externalities of the choice process.

Quantum frameness for CPT symmetry.

We develop a theory of charge-parity-time (CPT) frameness resources to circumvent CPT superselection. We construct and quantify such resources for spin-0, 1/2, 1, and Majorana particles and show that quantum information processing is possible even with CPT superselection. Our method employs a unitary representation of CPT inversion by considering the aggregate action of CPT rather than the composition of separate C, P, and T operations, as some of these operations involve problematic antiunitary representations.