Abstract
The theory of quantum Darwinism aims to explain how our objective classical reality arises from the quantum world, by analysing the distribution of information about a quantum system that is accessible to multiple observers, who probe the system by intercepting fragments of its environment. Previous work showed that, when the number of environmental fragments grows, the quantum channels modelling the information flow from system to observers become arbitrarily close—in terms of diamond norm distance—to ‘measure-and-prepare’ channels, ensuring objectivity of observables; the convergence is formalised by an upper bound on the diamond norm distance, which decreases with increasing number of fragments. Here, we derive tighter diamond norm bounds on the emergence of objectivity of observables for quantum systems of infinite dimension, providing an approach which can bridge between the finite- and the infinite-dimensional cases. Furthermore, we probe the tightness of our bounds by considering a specific model of a system-environment dynamics given by a pure loss channel. Finally, we generalise to infinite dimensions a result obtained by Brandão et al (2015 Nat. Commun. 6 7908), which provides an operational characterisation of quantum discord in terms of one-sided redistribution of correlations to many parties. Our results provide a unifying framework to benchmark quantitatively the rise of objectivity in the quantum-to-classical transition.
Highlights
Quantum theory has proven to be extremely successful in describing the physical laws of microscopic objects
In this paper we investigated the generic characteristics of the objectivity of observables arising in the quantum-to-classical transition within the premises of Quantum Darwinism
Going beyond recent studies for finite- and infinite-dimensional systems [30, 31], we presented a unified approach to derive bounds on the emergence of such objectivity in quantum systems of arbitrary dimension, probed by multiple observers each accessing a fragment of the environment
Summary
Quantum theory has proven to be extremely successful in describing the physical laws of microscopic objects. In [31], Knott et al overcame the finite-dimension restriction by showing that infinite-dimensional systems, under appropriate energy constraints, exhibit objectivity of observables Another interesting result in this context was recently obtained by Qi and Ranard [32]: they showed that, for finitedimensional systems, the set of channels which do not converge to objectivity is of fixed size O(1), instead of scaling with the number of environmental fragments N, as in [30, 31]. Objectivity of observables is regarded as emergent whenever the upper bound on the distance between channels representing the system-environment information flow and the measure-and-prepare ones goes to zero asymptotically. Some technical details behind our proofs are deferred to the Appendixes
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