Pointer states and quantum Darwinism with 2-body interactions

TL;DR

This paper investigates the conditions under which quantum systems with 2-body interactions can support classical objectivity through quantum Darwinism, highlighting the importance of separable interactions and the absence of intra-environmental interactions.

Contribution

It provides a comprehensive classification of 2-body interaction models and identifies key criteria for the emergence of pointer states and perfect quantum Darwinism.

Findings

Only models with separable system-environment interactions support pointer bases.

Perfect quantum Darwinism requires no intra-environmental interactions.

Information scrambling opposes the emergence of classical objectivity.

Abstract

Quantum Darwinism explains the emergence of classical objectivity within a quantum universe. However, to date most research in quantum Darwinism has focused on specific models and their stationary properties. To further our understanding of the quantum-to-classical transition it appears desirable to identify the general criteria a Hamiltonian has to fulfill to support classical reality. To this end, we categorize all models with 2-body interactions, and we show that only those with separable interaction of system and environment can support a pointer basis. We further show that "perfect" quantum Darwinism can only emerge if there are no intra-environmental interactions. Our analysis is complemented by the solution of the ensuing dynamics. We find that in systems that exhibit information scrambling, the dynamical emergence of classical objectivity is in direct competition with the non-local spread of quantum correlations. Our rigorous findings are illustrated with the numerical analysis of four representative models.