CLASSICAL-QUANTUM DIVERGENCES IN STRUCTURAL COMPLEXITIES OF MANY-BODY SYSTEMS

Abstract

The interactions between large numbers of interacting particles in complex environments give rise to a rich, diverse range of exotic phenomena such as emergent behaviours, phase transitions, and symmetry breaking. Studying the underlying structure and complexity of these systems helps us to understand these pervasive phenomena. Computational mechanics provides a constructive and systematic framework that identifies the intrinsic complexity present in stochastic systems. In this framework, the minimal memory required to model a given stochastic process -- known as the statistical complexity -- is a widely adopted quantifier of structure in complexity science. Here we use this framework to study the divergences in our perception of structure when we consider complexity from either quantum or classical perspectives – and the implications for quantifying resources in quantum systems. We study this question in the context of various many-body systems – classical and quantum Ising chains, and the one-dimensional Bose-Hubbard model.