Quantum homogenization and state randomization in semi-quantal spin systems

TL;DR

This paper studies semi-quantal spin systems where quantum bits interact via classical particles, showing that quantum homogenization occurs over time and leads to stationary bipartite entanglement, with the overall quantum state becoming a complete mixture.

Contribution

It demonstrates that quantum homogenization and state randomization occur in semi-quantal spin systems with classical particle motion, regardless of classical dynamics details.

Findings

Quantum homogenization occurs after sufficient time.

Stationary bipartite entanglement develops.

The quantum subsystem reaches a complete mixture when classical details are ignored.

Abstract

We investigate dynamics of semi-quantal spin systems in which quantum bits are attached to classically and possibly stochastically moving classical particles. The interaction between the quantum bits takes place when the respective classical particles get close to each other in space. We find that with Heisenberg XX couplings quantum homogenization takes place after a time long enough, regardless of the details of the underlying classical dynamics. This is accompanied by the development of a stationary bipartite entanglement. If the information on the details of the motion of a stochastic classical system is disregarded, the stationary state of the whole quantum subsystem is found to be a complete mixture in the studied cases, though the transients depend on the properties of the classical motion.