Emergence of the classical from the quantum substrate is a long-standing conundrum. The chapter describes its resolution based on three insights that stem from the recognition of the role of the environment. The chapter begins with the derivation of preferred states that define “events”, the essence of everyday classical reality. They arise from the tension between the unitary quantum dynamics and the nonlinear amplification inherent in replicating information. The resulting pointer states are consistent with these obtained via environment-induced superselection (einselection). They determine what can happen by defining events such as quantum jumps without appealing to Born’s rule for probabilities. Probabilities can be now deduced from envariance (a symmetry of entangled quantum states). With probabilities at hand one can quantify information flows accompanying decoherence. Effective amplification they represent explains perception of objective classical reality arising from within the quantum universe through redundancy of the pointer state records in their environment—through quantum Darwinism.
Emergence of the classical from the quantum substrate is a long-standing conundrum. The chapter describes its resolution based on three insights that stem from the recognition of the role of the environment. The chapter begins with the derivation of preferred states that define “events”, the essence of everyday classical reality. They arise from the tension between the unitary quantum dynamics and the nonlinear amplification inherent in replicating information. The resulting pointer states are consistent with these obtained via environment-induced superselection (einselection). They determine what can happen by defining events such as quantum jumps without appealing to Born’s rule for probabilities. Probabilities can be now deduced from envariance (a symmetry of entangled quantum states). With probabilities at hand one can quantify information flows accompanying decoherence. Effective amplification they represent explains perception of objective classical reality arising from within the quantum universe through redundancy of the pointer state records in their environment—through quantum Darwinism.
The emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. In this paper, I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the environment. I begin with the derivation of preferred sets of states that help to define what exists—our everyday classical reality. They emerge as a result of the breaking of the unitary symmetry of the Hilbert space which happens when the unitarity of quantum evolutions encounters nonlinearities inherent in the process of amplification—of replicating information. This derivation is accomplished without the usual tools of decoherence, and accounts for the appearance of quantum jumps and the emergence of preferred pointer states consistent with those obtained via environment-induced superselection, or einselection . The pointer states obtained in this way determine what can happen—define events—without appealing to Born’s Rule for probabilities. Therefore, p k =| ψ k | 2 can now be deduced from the entanglement-assisted invariance, or envariance —a symmetry of entangled quantum states. With probabilities at hand, one also gains new insights into the foundations of quantum statistical physics. Moreover, one can now analyse the information flows responsible for decoherence. These information flows explain how the perception of objective classical reality arises from the quantum substrate: the effective amplification that they represent accounts for the objective existence of the einselected states of macroscopic quantum systems through the redundancy of pointer state records in their environment—through quantum Darwinism . This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.
Core quantum postulates including the superposition principle and the unitarity of evolutions are natural and strikingly simple. I show that—when supplemented with a limited version of predictability (captured in the textbook accounts by the repeatability postulate)—these core postulates can account for all the symptoms of classicality. In particular, both objective classical reality and elusive information about reality arise, via quantum Darwinism, from the quantum substrate. This approach shares with the Relative State Interpretation of Everett the view that collapse of the wavepacket reflects perception of the state of the rest of the Universe relative to the state of observer’s records. However, our “let quantum be quantum” approach poses questions absent in Bohr’s Copenhagen Interpretation that relied on the preexisting classical domain. Thus, one is now forced to seek preferred, predictable, hence effectively classical but ultimately quantum states that allow observers keep reliable records. Without such (i) preferred basis relative states are simply “too relative”, and the ensuing basis ambiguity makes it difficult to identify events (e.g., measurement outcomes). Moreover, universal validity of quantum theory raises the issue of (ii) the origin of Born’s rule, pk=|ψk|2, relating probabilities and amplitudes (that is simply postulated in textbooks). Last not least, even preferred pointer states (defined by einselection—environment—induced superselection)—are still quantum. Therefore, unlike classical states that exist objectively, quantum states of an individual system cannot be found out by an initially ignorant observer through direct measurement without being disrupted. So, to complete the ‘quantum theory of the classical’ one must identify (iii) quantum origin of objective existence and explain how the information about objectively existing states can appear to be essentially inconsequential for them (as it does for states in Newtonian physics) and yet matter in other settings (e.g., thermodynamics). I show how the mathematical structure of quantum theory supplemented by the only uncontroversial measurement postulate (that demands immediate repeatability—hence, predictability) leads to preferred states. These (i) pointer states correspond to measurement outcomes. Their stability is a prerequisite for objective existence of effectively classical states and for events such as quantum jumps. Events at hand, one can now enquire about their probability—the probability of a pointer state (or of a measurement record). I show that the symmetry of entangled states—(ii) entanglement—assisted invariance or envariance—implies Born’s rule. Envariance also accounts for the loss of phase coherence between pointer states. Thus, decoherence can be traced to symmetries of entanglement and understood without its usual tool—reduced density matrices. A simple and manifestly noncircular derivation of pk=|ψk|2 follows. Monitoring of the system by its environment in course of decoherence typically leaves behind multiple copies of its pointer states in the environment. Only pointer states can survive decoherence and can spawn such plentiful information-theoretic progeny. This (iii) quantum Darwinism allows observers to use environment as a witness—to find out pointer states indirectly, leaving systems of interest untouched. Quantum Darwinism shows how epistemic and ontic (coexisting in epiontic quantum state) separate into robust objective existence of pointer states and detached information about them, giving rise to extantons—composite objects with system of interest in the core and multiple records of its pointer states in the halo comprising of environment subsystems (e.g., photons) which disseminates that information throughout the Universe.
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.
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.
Chapter 5 explores the consequences of decoherence. We live in a Universe that is fundamentally quantum. Yet, our everyday world appears to be resolutely classical. The aim of Chapter 5 is to discuss how preferred classical states, and, more generally, classical physics, arise, as an excellent approximation, on a macroscopic level of a quantum Universe. We show why quantum theory results in the familiar “classical reality” in open quantum systems, that is, systems interacting with their environments. We shall see how and why, and to what extent, quantum theory accounts for our classical perceptions. We shall not complete this task here—a more detailed analysis of how the information is acquired by observers is needed for that, and this task will be taken up in Part III of the book. Moreover, Chapter 5 shows that not just Newtonian physics but also equilibrium thermodynamics follows from the same symmetries of entanglement that led to Born’s rule (in Chapter 3).
Chapter 4 begins to discuss decoherence, and, thus, to address the overarching question: How does the classical world—classical states that are responsible for the objective reality of our everyday experience—emerge from within the Universe that is, as we know from compelling experimental evidence, made out of quantum stuff. The short answer to this question is that decoherence selects (from the vast number of superpositions that populate Hilbert space in the process of environment-induced superselection (also known as einselection) the few states that are—in contrast to all the other alternatives—stable in spite of their immersion in the environment. Decoherence is illustrated with a detailed discussion of two models. A spin decohered by an environment of spins as well as quantum Brownian motion have become paradigmatic models of decoherence for good reason: They are exactly solvable and yet they capture (albeit in an idealized manner) the emergence of the preferred classical states in settings that are relevant for quantum measurements and for Newtonian dynamics in effectively classical phase space.