The objective, classical world emerges from the underlying quantum substrate via the proliferation of redundant copies of selected information into the environment, which acts as a communication channel, transmitting that information to observers. These copies are independently accessible, allowing many observers to reach consensus about the state of a quantum system via its imprints in the environment. Quantum Darwinism recognizes that the redundancy of information is thus central to the emergence of objective reality in the quantum world. However, in addition to the quantum system of interest,'' there are many other systems of no interest'' in the Universe that can imprint information on the common environment. There is therefore a danger that the information of interest will be diluted with irrelevant bits, suppressing the redundancy responsible for objectivity. We show that mixing of the relevant (the wheat'') and irrelevant (the chaff'') bits of information makes little quantitative difference to the redundancy of the information of interest. Thus, we demonstrate that it does not matter whether one separates the wheat (relevant information) from the (irrelevant) chaff: The large redundancy of the relevant information survives dilution, providing evidence of the objective, effectively classical world.
Quantum Darwinism provides an information-theoretic framework for the emergence of the objective, classical world from the quantum substrate. The key to this emergence is the proliferation of redundant information throughout the environment where observers can then intercept it. We study this process for a purely decohering interaction when the environment,
E, is in a nonideal (e.g., mixed) initial state. In the case of good decoherence, that is, after the pointer states have been unambiguously selected, the mutual information between the system,
S, and an environment fragment,
F, is given solely by
F's entropy increase. This demonstrates that the environment's capacity for recording the state of
S is directly related to its ability to increase its entropy. Environments that remain nearly invariant under the interaction with
S, either because they have a large initial entropy or a misaligned initial state, therefore have a diminished ability to acquire information. To elucidate the concept of good decoherence, we show that, when decoherence is not complete, the deviation of the mutual information from
F's entropy change is quantified by the quantum discord, i.e., the excess mutual information between
S and
F is information regarding the initial coherence between pointer states of
S. In addition to illustrating these results with a single-qubit system interacting with a multiqubit environment, we find scaling relations for the redundancy of information acquired by the environment that display a universal behavior independent of the initial state of
S. Our results demonstrate that Quantum Darwinism is robust with respect to nonideal initial states of the environment: the environment almost always acquires redundant information about the system but its rate of acquisition can be reduced.
We study the role of the information deposited in the environment of an open quantum system in the course of the decoherence process. Redundant spreading of information---the fact that some observables of the system can be independently read off from many distinct fragments of the environment---is investigated as the key to effective objectivity, the essential ingredient of classical reality. This focus on the environment as a communication channel through which observers learn about physical systems underscores the importance of quantum Darwinism---selective proliferation of information about ``the fittest states'' chosen by the dynamics of decoherence at the expense of their superpositions---as redundancy imposes the existence of preferred observables. We demonstrate that the only observables that can leave multiple imprints in the environment are the familiar pointer observables singled out by environment-induced superselection (einselection) for their predictability. Many independent observers monitoring the environment will therefore agree on properties of the system as they can only learn about preferred observables. In this operational sense, the selective spreading of information leads to appearance of an objective classical reality from within the quantum substrate.
Quantum Darwinism demonstrates not only that preferred states are selected for their stability but also that information about them is broadcast by the same environment that causes decoherence and einselection. That environment acts both as a censor and as an advertising agent that disseminates information about pointer states while suppressing complementary information. Chapter 8 explores the implications and limitations of quantum Darwinism using models inspired by the structure of the Universe we inhabit. We perceive our Universe using light and other means of information transmission. We explore models that have a well-defined relation with our everyday reality, and where one can also selectively relax some of the idealized assumptions and investigate the consequences. Light is the communication channel through which we obtain most of our information. Fortunately, it is an ideal channel in the sense of quantum Darwinism, and simple but realistic cases are exactly solvable. The solution presented herein demonstrates the inevitability of the consensus between observers who rely on scattered photons: The emergence of classical objective reality (classical because pointer states are einselected, and objective because redundancy imposes consensus) is inevitable. This is how the classical world we perceive emerges from within the quantum Universe we inhabit.
Quantum Darwinism recognizes that decoherence imprints redundant records of preferred quasi-classical pointer states on the environment. These redundant records are then accessed by observers. We show how redundancy enables and even implies consensus between observers who use fragments of that decohering environment to acquire information about systems of interest. We quantify consensus using information-theoretic measures that employ mutual information to assess the correlation between the records available to observers from distinct -- hence, independently accessible -- fragments of the environment. We prove that when these fragments have enough information about a system, observers that access them will attribute the same pointer state to that system. Thus, those who know enough about the system agree about what they know. We then test proposed measures of consensus in a solvable model of decoherence as well as in numerical simulations of a many-body system. These results provide detailed understanding of how our classical everyday world arises from within the fundamentally quantum Universe we inhabit.
Quantum Darwinism recognizes the role of the environment as a communication channel: Decoherence can selectively amplify information about the pointer states of a system of interest (preventing access to complementary information about their superpositions) and can make records of this information accessible to many observers. This redundancy explains the emergence of objective, classical reality in our quantum Universe. Here, we demonstrate that the amplification of information in realistic spin environments can be quantified by the quantum Chernoff information, which characterizes the distinguishability of partial records in individual environment subsystems. We show that, except for a set of initial states of measure zero, the environment always acquires redundant information. Moreover, the Chernoff information captures the rich behavior of amplification in both finite and infinite spin environments, from quadratic growth of the redundancy to oscillatory behavior. These results will considerably simplify experimental testing of quantum Darwinism, e.g., using nitrogen vacancies in diamond.
Quantum Darwinism is a leading framework for explaining how classical reality emerges from a quantum universe—the environment redundantly encodes the pointer state information of quantum systems, enabling multiple independent observers to reach consensus about reality. However, a fundamental question has remained unanswered: Why does the environment possess this capacity for redundant recording? This paper proposes, within the information-potential conversion framework, that the redundant recording mechanism of quantum Darwinism is the physical realization of the information-potential conversion consensus protocol—the environment, acting as the physical medium for information-potential conversion, redundantly encodes system information, providing consistent conversion records for independent information processing units, from which classical reality emerges. Based on this interpretation, three testable quantitative predictions are proposed: (1) In superconducting quantum circuits, when system complexity exceeds a critical threshold, the efficiency of redundant recording should exhibit an abrupt transition—a signal of the information-potential conversion phase transition of the consensus protocol from “quantum critical” to “classically locked”; (2) There should exist a precise linear relationship between functional information and information-potential conversion energy consumption: each additional bit of functional information doubles the minimum heat dissipation required for record stabilization; (3) Consensus strength—the stability of classical reality—should be positively correlated with the number of information processing units participating in the consensus protocol, and a critical number exists at which the consensus phase transition occurs. quantum Darwinism, information-potential conversion, consensus protocol, classical emergence, redundant recording, functional information