Quantum Coarse-Graining, Symmetries and Reducibility of Dynamics

TL;DR

This paper explores how coarse-graining the state space in quantum systems can reduce complexity by identifying broader symmetries that facilitate dynamics reduction, extending beyond traditional Noether symmetries.

Contribution

It introduces a quantum notion of state-space coarse-graining and establishes conditions for dynamics reducibility, revealing new symmetries that aid in complexity reduction.

Findings

Broader class of symmetries identified beyond Noether's theorem

Quantum coarse-graining allows marginalization of degrees of freedom

Conditions for reducibility of dynamics in quantum systems derived

Abstract

The common idea behind complexity reduction in physical systems is separation of information into "physically meaningful" and "safely ignorable". Here we consider a generic notion of such separation -- implemented by coarse-graining the state-space -- and address the question of what information is indeed safely ignorable if we want to reduce the complexity of dynamics. The general condition for reducibility of dynamics under coarse-graining will be presented for stochastic and quantum systems. In the process we develop the quantum notion of state-space coarse-graining that allows to marginalize selected degrees of freedom. One of our main findings is that there is a broader class of symmetries, beyond those that are considered by Noether's Theorem, that can play a role in the reduction of dynamics. Some examples of quantum coarse-grainings and the reduction of dynamics with symmetries will be discussed.