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

Roberto D Baldijao,Andrew J P Garner,Marius Krumm,Markus P Mueller

doi:10.22331/q-2022-01-31-636

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.

Highlights

Quantum Darwinism [1,2,3,4,5,6,7,8,9,10,11,12] addresses one of the toughest questions raised by quantum theory: If the universe is fundamentally described by quantum mechanics, how does an objective classical world arise? At the heart of this question is a tension between the microscopic quantum realm, in which systems happily exist in states of super-imposed possibility, and the macroscopic world of “classical” systems, which are only ever observed in definite objective states
Quantum Darwinism provides a mechanism through which crucial aspects of classicality can be understood to emerge in the quantum domain [1,2,3,4,5]
We generalized an idealized notion of Darwinism, where maximal classical information is perfectly broadcast to an environment split into fractions, to the framework of generalized probabilistic theories (GPTs)

Summary

Introduction

Quantum Darwinism [1,2,3,4,5,6,7,8,9,10,11,12] addresses one of the toughest questions raised by quantum theory: If the universe is fundamentally described by quantum mechanics, how does an objective classical world arise? At the heart of this question is a tension between the microscopic quantum realm, in which systems happily exist in states of super-imposed possibility, and the macroscopic world of “classical” systems (such as the pointer needle of a read-out gauge), which are only ever observed in definite objective states. We adopt the minimal–assumptions framework of generalized probabilistic theories (GPTs) [17, 18] These encompass a wide class of operational scenarios, in which a physical system is entirely characterized by its experimental statistics resulting from preparation and subsequent measurement procedures. Something can still be learned about S – perhaps because the interaction induces certain quantum states on system and environment such that measurements made on S and {En} in the right choice of basis yield correlated outcomes. This interaction must preserve some aspect of the initial state of S, so that what the environment learns can be considered as being about S. It does not imply that these environment states have the same physical properties as the corresponding state of the main system or of the other environment systems.) Consider the

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Results

Conclusion