Emergence of the Quantum from the Classical

Anthony Kiely, Diana A. Chisholm, Akram Touil +3 more

We present a precise characterization of the onset of classicality that combines the formalism of quantum Darwinism with the tools from quantum metrology. We show that the quantum Fisher information provides a useful metric for assessing the rate at which classical objectivity emerges. Furthermore, our formalism allows us to explore how the choice of measurement impacts the precision with which an observer can determine the state of the system. For a paradigmatic example of the spin-star model, we demonstrate that optimal measurements lead to the emergence of classicality at an exponential rate. Although other measurements necessarily lead to slower emergence, we importantly show that suboptimal measurements can still saturate the Cramér-Rao bound. By recasting emergent classicality as an information acquisition protocol, our framework provides a precise operational description of quantum Darwinism.

Wojciech Hubert Zurek

Луценко Евгений Вениаминович, Трунев Александр Петрович

In this article we give a generalization of Hartley's model for the measure of information. We propose a rate of emergence, which is applicable to systems obeying classical or quantum statistics. Quantum systems that obey Fermi-Dirac statistics and Bose-Einstein condensate, as well as classical systems obeying the Maxwell-Boltzmann statistics have been considered. We found that the emergence parameter of quantum and classical systems differ as well as the emergence parameter of quantum systems of fermions and bosons. Consequently, the emergence parameter might be used to distinguish the classical system and quantum system, as well as quantum system of fermions and the quantum system of bosons

Tabish Qureshi

Fernando G. S. L. Brandão, Marco Piani, Paweł Horodecki

Quantum Darwinism posits that only specific information about a quantum system that is redundantly proliferated to many parts of its environment becomes accessible and objective, leading to the emergence of classical reality. However, it is not clear under what conditions this mechanism holds true. Here we prove that the emergence of classical features along the lines of quantum Darwinism is a general feature of any quantum dynamics: observers who acquire information indirectly through the environment have effective access at most to classical information about one and the same measurement of the quantum system. Our analysis does not rely on a strict conceptual splitting between a system-of-interest and its environment, and allows one to interpret any system as part of the environment of any other system. Finally, our approach leads to a full operational characterization of quantum discord in terms of local redistribution of correlations. Quantum Darwinism provides an explanation for the emergence of classical reality from the underlying quantum world, as information proliferates in the environment and becomes objective. Here, the authors show how some aspects of this mechanism is generic and classicality emerges for any quantum dynamics.

E. U. Condon