Quantum Darwinism and the spreading of classical information in non-classical theories

TL;DR

This paper investigates the physical principles enabling classical information spreading in quantum Darwinism within probabilistic theories, revealing that entanglement is essential for the emergence of classical reality in non-classical theories.

Contribution

It formulates the simplest Darwinism interactions in probabilistic theories and identifies conditions under which non-classical theories can exhibit classical information spreading.

Findings

Entanglement is necessary for classical information spreading in non-classical theories.

Spekkens' toy theory admits Darwinism-like spreading of classical information.

Theories with certain symmetries or decoherence processes can also support this mechanism.

Abstract

Quantum Darwinism posits that the emergence of a classical reality relies on the spreading of classical information from a quantum system to many parts of its environment. But what are the essential physical principles of quantum theory that make this mechanism possible? We address this question by formulating the simplest instance of Darwinism - CNOT-like fan-out interactions - in a class of probabilistic theories that contain classical and quantum theory as special cases. We determine necessary and sufficient conditions for any theory to admit such interactions. We find that every theory with non-classical features that admits this idealized spreading of classical information must have both entangled states and entangled measurements. Furthermore, we show that Spekkens' toy theory admits this form of Darwinism, and so do all probabilistic theories that satisfy principles like strong symmetry, or contain a certain type of decoherence processes. Our result suggests the counter-intuitive general principle that in the presence of local non-classicality, a classical world can only emerge if this non-classicality can be "amplified" to a form of entanglement.