Toy Model Challenging Prevailing Definitions of Classicality

TL;DR

This paper presents a toy model that challenges the adequacy of current criteria for classicality, showing that classical behavior can be fragile and reconverge, questioning the sufficiency of existing definitions.

Contribution

It introduces a toy model demonstrating that quantum Darwinism and decoherence criteria alone do not guarantee stable classicality, highlighting the need for more robust definitions.

Findings

Classical dynamics can be fragile and reconverge after control operations.

Quantum Darwinism can coexist with non-Markovian dynamics.

Current criteria may be insufficient for defining classicality.

Abstract

We analyze a toy model that obeys environmentally induced decoherence and quantum Darwinism and satisfies the decoherent histories criterion and Leggett-Garg inequalities with respect to the pointer basis. Yet, the resulting "classical" dynamics are extremely fragile and recohere after a seemingly innocent control operation. This challenges the idea that classical behaviour or the Multiverse branches can be identified by looking at the universal wave function alone. It also demonstrates that quantum Darwinism is compatible with strong non-Markovianity. Possible solutions related to Markovianity, non-integrability and an operational definition of pointer states are briefly discussed.