Operational Quantum Mereology: an Information Scrambling Approach

The ability of dividing a physical system into its smaller parts is a key aspect of the scientific reductionist method. It allows one to understand the behavior of complex systems in terms of fundamental, simpler components and their interrelations and dynamical interactions. For quantum systems this division can be performed in a multitude of ways depending on the experimental resources available, the operational constraints and on the pursued objectives. The aim of this project is the development of a unified, conceptual and mathematical, framework for the optimal selection of quantum "subsystems”. This will help the progress of Quantum Sciences and possibly the deployment of transformative novel quantum technologies. The project has also important educational and training components as it will involve, in an essential fashion, graduate students. This will facilitate their future enrollment into the national, academic as well industrial, quantum workforces. The technical approach will be based on the notion of "information scrambling” which is the way in which information, initially encoded on a definite and localized set of degrees of freedoms, gets quickly "lost” by its uncontrollable spreading over an increasingly large and delocalized set of degrees of freedom. A toolkit of novel mathematical tools will be designed to quantitatively measure the character, the speed and strength of this scrambling processes. Once this is achieved, the tools will be deployed to determine the optimal division of interesting many body systems into parts based on a minimal scrambling criterion. The latter is conceptually a sort of “minimal entropy production” principle telling us that the "emergent” subsystems are those more resilient to environmental noise and can then preserve their informational identity for the longest times. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.