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arXiv:quant-ph/0408125 · Physical Review A

Environment as a witness: Selective proliferation of information and emergence of objectivity in a quantum universe

Harold Ollivier, David Poulin, Wojciech Hubert Zurek

Published Oct 31, 2005• 127 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.72.042113

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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.
We study the emergence of objective properties of quantum systems caused by their interaction with an environment. In our analysis, the environment is promoted from a passive role of a reservoir selectively destroying quantum coherence to a communication channel through which observers find out about the Universe. We show that only preferred pointer states of the system can leave a redundant and easily detectable imprint on the environment. Observers who -- as it is almost always the case -- discover the state of the system indirectly (by monitoring a fraction of its environment) find out only about the corresponding pointer observable, and can do that without perturbing the system. Many observers acting independently in this fashion will agree about its state: in this operational sense, preferred pointer states exist objectively.
We study the emergence of objective properties in open quantum systems. In our analysis, the environment is promoted from a passive role of a reservoir selectively destroying quantum coherence to an active role of amplifier selectively proliferating information about the system. We show that only preferred pointer states of the system can leave a redundant and therefore easily detectable imprint on the environment. Observers who-as is almost always the case-discover the state of the system indirectly (by probing a fraction of its environment) will find out only about the corresponding pointer observable. Many observers can act in this fashion independently and without perturbing the system. They will agree about its state. In this operational sense, preferred pointer states exist objectively.
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.
The aim in Chapter 7 is to take into account the role of the means of information transmission on the nature of the states that can be perceived. Our point of departure is the recognition that the information we obtain is acquired by observers who monitor fragments of the same environment that decohered the system, einselecting preferred pointer states in the process. Moreover, we only intercept a fraction of the environment. The only information about the system that can be transmitted by its fraction must have been reproduced in many copies in that environment. This process of amplification limits what can be found out to the states einselected by decoherence. Quantum Darwinism provides a simple and natural explanation of this restriction, and, hence, of the objective existence—the essence of classicality—for the einselected states. This chapter introduces and develops information-theoretic tools and concepts (including, e.g., redundancy) that allow one to explore and characterize correlations and information flows between systems, environments, and observers, and illustrates them on an exactly solvable yet non-trivial model.
The roles of decoherence and environment–induced superselection in the emergence of the classical from the quantum substrate are described. The stability of correlations between the einselected quantum pointer states and the environment allows them to exist almost as objectively as classical states were once thought to exist: there are ways of finding out what is the pointer state of the system which uses redundancy of their correlations with the environment, and which leave einselected states essentially unperturbed. This relatively objective existence of certain quantum states facilitates operational definition of probabilities in the quantum setting. Moreover, once there are states that ‘exist’and can be ‘found out’, a ‘collapse’ in the traditional sense is no longer necessary—–in effect, it has already happened. The records of the observer will contain evidence of an effective collapse. The role of the preferred states in the processing and storage of information is emphasized. The existential interpretation based on the relatively objective existence of stable correlations between the einselected states of observers memory and in the outside universe is formulated and discussed.
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.