The Rise and Fall of Redundancy in Decoherence and Quantum Darwinism

TL;DR

This paper investigates how quantum correlations evolve in many-body systems, showing that typical states exhibit non-classical correlations and that the emergence of classical objectivity via quantum Darwinism is exceptional and can be suppressed by dynamics.

Contribution

It analyzes the conditions for the formation and decay of redundant, classical-like states in quantum systems, extending understanding of decoherence and quantum Darwinism.

Findings

Highly non-classical correlations are typical in random states.

Redundant, classical-like states are exceptional and not generic.

Dynamics can suppress redundancy to levels of random states on relaxation timescales.

Abstract

A state selected at random from the Hilbert space of a many-body system is overwhelmingly likely to exhibit highly non-classical correlations. For these typical states, half of the environment must be measured by an observer to determine the state of a given subsystem. The objectivity of classical reality-the fact that multiple observers can agree on the state of a subsystem after measuring just a small fraction of its environment-implies that the correlations found in nature between macroscopic systems and their environments are very exceptional. Building on previous studies of quantum Darwinism showing that highly redundant branching states are produced ubiquitously during pure decoherence, we examine conditions needed for the creation of branching states and study their demise through many-body interactions. We show that even constrained dynamics can suppress redundancy to the values typical of random states on relaxation timescales, and prove that these results hold exactly in the thermodynamic limit.