Emergence of noncontextuality under quantum Darwinism

TL;DR

This paper demonstrates that under certain conditions, the objectivity emerging from quantum Darwinism aligns with classical noncontextuality, establishing a threshold for when classicality can be said to have emerged.

Contribution

It connects quantum Darwinism with Spekkens' noncontextuality, providing a criterion for the emergence of classical objectivity based on information encoding.

Findings

Objectivity in quantum Darwinism can be classical if environment encodes information sufficiently well.

A threshold on information encoding determines when classical objectivity emerges.

Noncontextuality serves as a criterion for classicality in quantum Darwinism.

Abstract

Quantum Darwinism proposes that the proliferation of redundant information plays a major role in the emergence of objectivity out of the quantum world. Is this kind of objectivity necessarily classical? We show that if one takes Spekkens' notion of noncontextuality as the notion of classicality and the approach of Brand\~{a}o, Piani and Horodecki to quantum Darwinism, the answer to the above question is `yes', if the environment encodes sufficiently well the proliferated information. Moreover, we propose a threshold on this encoding, above which one can unambiguously say that classical objectivity has emerged under quantum Darwinism.