Modelling quantum measurement dynamics: from decoherence to redundancy with site-hopping indistinguishable particles
Abstract
In recent years, new theoretical insights into decoherence and quantum measurements have emerged through the study of many-body dynamics in isolated quantum systems. It is now understood that the parameters and energy scales in system-environment interactions decisively affect how readily information spreads from a quantum system into its surroundings during a decoherence event. A popular choice for studying these effects is the framework of quantum Darwinism (QD), but so far few works have applied this to realistic many-body models. Inspired by experimentally-accessible setups, in this work we introduce a simple, flexible, numerically exact many-body model of a system broadcasting information into an environment: a 1D lattice of sites with hopping particles. We show that different choices of parameters lead to the recovery of known scenarios featuring different decoherence and QD effects, such as equilibration, revivals of coherence, and redundancy. In constructing this model we resolve the crucial issue of indistinguishability: we explain how to calculate the entropy of a fraction of the environment when said environment is composed of indistinguishable fermions or bosons (or lattice sites containing them). We then show that particle statistics can make a notable difference to the QD properties of the setup, with fermionic environments sometimes achieving redundancy much more readily than bosonic or site-based ones. Our work opens the door to much closer alignment between theoretical models and experimental tests of the dynamics of quantum measurements and the quantum-to-classical transition.