Zenith Grant Awardee

Andrew J P Garner

National University of Singapore

Co-Investigators

Vlatko Vedral, National University of Singapore

Project Title

Observer-dependent complexity: The quantum-classical divergence over \'what is complex?\'

Project Summary

The most interesting phenomena are complex, lying at the border between order and chaos. Complex systems exhibit rich behaviour, from emergence and self-organization to the ability to perform universal computation. Understanding complexity is thus considered essential to describe nearly all non-trivial phenomena around us, from phase transitions in the physical sciences to life itself. A fundamental concern in complexity science is to formalize our intuition of ‚\"what is complex?\", into quantifiable values. Statistical complexity achieves this by asking \"How much memory must an observer maintain to understand a process?\",It has been recently established that the answer to this depends not only on the complex system itself, but also on properties of the observer, who judges the system — especially if one observer has access to the power of quantum information. This could herald entirely new ways for complexity to behave, opening a new paradigm where \"what is complex?\", fundamentally depends on the physics of the observer. Our project establishes this by providing a formal framework for the physics of the observer. We examine the extent to which observers can disagree about complexity, and ascertain the consequences of their disagreement, including both in their thermal behaviour and impact on causality.

Technical Abstract

Complex systems, such as neural networks, fractals and living organisms, display a remarkable range of unique phenomena such as self-organization, evolution and emergence. As such, their study informs a wide range of foundational issues, including the origins and development of life, the arrow of time, and even questions of consciousness. A fundamental requirement of complexity science is to be able to identify what is complex. Statistical complexity achieves this by asking \"How much memory an observer must maintain in order to understand such phenomena?\" However, recent studies show that answer to this depends not only on the system, but changes depending on the type of observer recording the data: a classical observer may judge the system to be fundamentally more complex than one who uses quantum information processing. This observer-dependence opens a new paradigm in complexity science, in which it is imperative to understand the physics of the observer. In this project, using tools from quantum information theory and complexity science, we will build a rigorous mathematical understanding of the observer in the context of complexity. This shall include consideration of the extent of divergence, the thermodynamic consequences of observation, and the links between observation and causality in complex systems.