  We examine the hypothesis that consciousness can be understood as a state of
matter, "perceptronium", with distinctive information processing abilities. We
explore five basic principles that may distinguish conscious matter from other
physical systems such as solids, liquids and gases: the information,
integration, independence, dynamics and utility principles. If such principles
can identify conscious entities, then they can help solve the quantum
factorization problem: why do conscious observers like us perceive the
particular Hilbert space factorization corresponding to classical space (rather
than Fourier space, say), and more generally, why do we perceive the world
around us as a dynamic hierarchy of objects that are strongly integrated and
relatively independent? Tensor factorization of matrices is found to play a
central role, and our technical results include a theorem about Hamiltonian
separability (defined using Hilbert-Schmidt superoperators) being maximized in
the energy eigenbasis. Our approach generalizes Giulio Tononi's integrated
information framework for neural-network-based consciousness to arbitrary
quantum systems, and we find interesting links to error-correcting codes,
condensed matter criticality, and the Quantum Darwinism program, as well as an
interesting connection between the emergence of consciousness and the emergence
of time.
