Towards quantifying complexity with quantum mechanics
Abstract
While we have intuitive notions of structure and complexity, the formalization of this intuition is nontrivial. The statistical complexity is a popular candidate. It is based on the idea that the complexity of a process can be quantified by the complexity of its simplest mathematical model —the model that requires the least past information for optimal future prediction. Here we review how such models, known as machines can be further simplified through quantum logic, and explore the resulting consequences for understanding complexity. In particular, we propose a new measure of complexity based on quantum machines. We apply this to a simple system undergoing constant thermalization. The resulting quantum measure of complexity aligns more closely with our intuition of how complexity should behave.
 Publication:

European Physical Journal Plus
 Pub Date:
 September 2014
 DOI:
 10.1140/epjp/i2014141912
 arXiv:
 arXiv:1404.6255
 Bibcode:
 2014EPJP..129..191T
 Keywords:

 Quantum Physics
 EPrint:
 10 pages, 6 figure, Published in the Focus Point on Quantum information and complexity edition of EPJ Plus