Abstract
The grand quest for a scientific understanding of consciousness has given rise to many new theoretical and empirical paradigms for investigating the phenomenology of consciousness as well as clinical disorders associated to it. A major challenge in this field is to formalize computational measures that can reliably quantify global brain states from data. In particular, information-theoretic complexity measures such as integrated information have been proposed as measures of conscious awareness. This suggests a new framework to quantitatively classify states of consciousness. However, it has proven increasingly difficult to apply these complexity measures to realistic brain networks. In part, this is due to high computational costs incurred when implementing these measures on realistically large network dimensions. Nonetheless, complexity measures for quantifying states of consciousness are important for assisting clinical diagnosis and therapy. This article is meant to serve as a lookup table of measures of consciousness, with particular emphasis on clinical applicability. We consider both, principle-based complexity measures as well as empirical measures tested on patients. We address challenges facing these measures with regard to realistic brain networks, and where necessary, suggest possible resolutions.