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This chapter presents some concluding thoughts from the authors. It evokes future prospects and mentions the challenges ahead. It addresses questions such as: How far will the industry of thought experiments be carried and the quantum classical boundary pushed back? What are the odds to beat decoherence and make quantum information practical? What are the best systems to achieve these goals? Should they be reached from bottom-up, as in atomic physics, or from top-down, as in condensed matter physics?

This chapter deals with the important field of environment-induced decoherence and the transition to the classical behaviour of open quantum systems. A number of techniques is developed that allows the determination of decoherence time scales. The decoherence behaviour in several Markovian models is investigated in detail, such as vacuum and thermal decoherence, decoherence in quantum Brownian motion, and the destruction of coherence through internal degrees of freedom and through the scattering of environmental particles. Moreover, experiments on the decoherence of Schrödinger cat states of the electromagnetic field are discussed, as well as the non-Markovian destruction of quantum coherence in the Caldeira–Leggett model, and the environment-induced selection of a pointer basis in the quantum theory of measurement.

This chapter is concerned with the technical details of how emergent branching occurs in the Everett interpretation. Accordingly, its focus is on decoherence theory, the branch of quantum physics which studies the effects on macroscopic degrees of freedom of their environment (whether that environment is internal or external). The chapter reviews decoherence theory in a self-contained manner, beginning with the ‘environment-induced decoherence’ approach developed by Joos, Zeh and zurek, and moving on to the more abstract approach of Gell-Mann, Hartle, and Halliwell. The chapter shows that decoherence, in the context of the Everett interpretation, does indeed cause the quantum world to develop an emergent branching structure, though this branching structure is continuous and resists any attempt to quantify the precise number of branches.

This chapter describes three insights into the transition from quantum to classical that are based on the recognition of the role of the environment. It starts with a minimalist derivation of preferred sets of states. This breaking of the unitary symmetry of the Hilbert space yields — without the usual tools of decoherence — quantum jumps and pointer states consistent with those obtained via einselection. Pointer states obtained this way dene events without appealing to Born's rule for probabilities, which can be now derived from envariance-symmetry of entangled quantum states. With probabilities at hand one can analyze information flows in the course of decoherence. They explain how classical reality can arise from the quantum substrate by accounting for the objective existence of the einselected states of quantum systems through the redundancy of pointer state records in their environment — through quantum Darwinism. Taken together, and in the right order, these three advances (which fit well within Everett's relative states framework, but do not require ‘many worlds’ per se) extend the existential interpretation of quantum theory.

This chapter argues that the intractable part of the measurement problem — the ‘big’ measurement problem — is a pseudo-problem that depends for its legitimacy on the acceptance of two dogmas. The first dogma is John Bell's assertion that measurement should never be introduced as a primitive process in a fundamental mechanical theory like classical or quantum mechanics, but should always be open to a complete analysis, in principle, of how the individual outcomes come about dynamically. The second dogma is the view that the quantum state has an ontological significance analogous to the significance of the classical state as the ‘truthmaker’ for propositions about the occurrence and non-occurrence of events, i.e., that the quantum state is a representation of physical reality. The chapter shows how both dogmas can be rejected in a realist information-theoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. The Everettian, too, regards the ‘big’ measurement problem as a pseudo-problem, because the Everettian rejects the assumption that measurements have definite outcomes, in the sense that one particular outcome, as opposed to other possible outcomes, actually occurs in a quantum measurement process. By contrast with the Everettians, the chapter accepts that measurements have definite outcomes. By contrast with the Bohmians and the GRW ‘collapse’ theorists who add structure to the theory and propose dynamical solutions to the ‘big’ measurement problem, we take the problem to arise from the failure to see the significance of Hilbert space as a new kinematic framework for the physics of an indeterministic universe, in the sense that Hilbert space imposes kinematic (i.e., pre-dynamic) objective probabilistic constraints on correlations between events.

This chapter replies to claims that the pilot-wave theory of de Broglie and Bohm is really a many-worlds theory with a superfluous configuration appended to one of the worlds. Assuming that pilot-wave theory does contain an ontological pilot wave (a complex-valued field in configuration space), the chapter shows that such claims arise from not interpreting pilot-wave theory on its own terms. Specifically, the theory has its own (‘subquantum’) theory of measurement, and in general describes a ‘non-equilibrium’ state that violates the Born rule. Furthermore, in realistic models of the classical limit, one does not obtain localised pieces of an ontological pilot wave following alternative macroscopic trajectories: from a de Broglie–Bohm viewpoint, alternative trajectories are merely mathematical and not ontological. Thus, from the perspective of pilot-wave theory itself, many worlds is an illusion. It is further argued that, even leaving pilot-wave theory aside, the theory of many worlds is rooted in the intrinsically unlikely assumption that quantum measurements should be modelled on classical measurements, and is therefore unlikely to be true.

This introductory chapter summarizes the principal positive theses of the book (Section 1), namely, that the unitary evolution of the quantum state, for sufficiently large systems of particles in thermal environments, yields a multiplicity of branching structures (worlds) obeying approximately classical equations, a result that follows from decoherence theory with no special assumptions or additions to the quantum formalism; and that further, the branching of worlds has a natural interpretation in terms of probability, as quantified by the Born rule in terms of ratios of squared norms of branch amplitudes. In particular, an agent who knows the branching structures of the quantum state that will result from his actions is rationally compelled to order his preferences among actions by the expected utilities of those branching structures as defined by the Born rule. He is, moreover, entitled to view a branching process as involving uncertainty as to which branch he will find himself. But independent of the truth of these claims, the theory is still testable: an agent who does not know the branching structure of the state, and who is indeed undecided between a many-worlds and a one-world theory, is rationally bound to update her credences in such theories by conditionalisation on observed statistical evidence, just as she is bound to do in the case of conventional quantum mechanics. Section 2 summarizes some of the arguments and counter-arguments for these claims as developed in subsequent chapters. Section 3 provides some more mathematical and historical background to the Everett interpretation, including a brief introduction to the decoherent histories formalism.

This chapter argues for the view that the Everett (‘many worlds’) interpretation is nothing more or less than a literal reading of the formalism of unitary quantum mechanics. The central component of this story is decoherence: the process by which the evolution of the quantum state acquires a branching structure. The chapter gives a conceptual introduction to decoherence and its conceptual role, emphasizing the significance of its effects on the dynamics of degrees of freedom which are undergoing decoherence. It then argues that, although the branching structure generated by decoherence is ‘for all practical purposes’ in the sense that it is not part of the microscopic formalism of quantum theory, nonetheless it is a perfectly real, observer-independent feature of reality — it is emergent from that microscopic formalism in a way very familiar from many other parts of science.

Macroscopic systems are described most completely by local densities (particle number, momentum, and energy) yet the superposition states of such physical variables, indicated by the Everett interpretation, are not observed. In order to explain this, it is argued that histories of local number, momentum, and energy density are approximately decoherent when coarse-grained over sufficiently large volumes. Decoherence arises directly from the proximity of these variables to exactly conserved quantities (which are exactly decoherent), and not from environmentally induced decoherence. This chapter discusses the approach to local equilibrium and the subsequent emergence of hydrodynamic equations for the local densities. The results are general but the chapter focuses on a chain of oscillators as a specific example in which explicit calculations may be carried out. It discusses the relationships between environmentally-induced and conservation-induced decoherence, and presents a unified view of these two mechanisms.

This chapter focuses on coherence and decoherence, starting from the basis of quantum mechanics and including the classical paradox of Schrödinger’s cat and entanglement. Decoherence and relaxation are simultaneously accounted for by an evolution equation for the density matrix, which is analysed in the case of spin tunnelling and simplifies when decoherence is complete. The final section discusses the possible exploitation of coherence in quantum computing.

A thoroughgoing and consistent application of quantum theory shows that the connection between classical and quantum physics is very different from what can be found in standard textbooks. In the last two decades it has been shown that the elements of classical physics emerge through an irreversible quantum process called ‘decoherence’. According to decoherence theories, quantum objects acquire classical properties only through interactions with their natural environment as a consequence of the holistic features of quantum theory. In view of the interpretation problem of quantum theory, only two directions out of the host of proposals suggested in the course of time appear to remain consistent solutions. Whatever solution is preferred, the message of decoherence remains the same: classical notions are not needed as the starting point for physics. Instead, these emerge through the dynamical process of decoherence from the quantum substrate.

The interference of electron waves in nanostructures adds clear fingerprints of quantum mechanical behavior to electronic transport in semiconductor nanostructures. This chapter discusses the Aharonov–Bohm effect as one of the most fundamental interference effects. It introduces the notion of the Aharonov–Bohm phase, and contrasts Aharonov–Bohm oscillations with Altshuler–Aronov–Spivak oscillations. Geometric phase effects are discussed based on Berry's phase, the Aharonov–Casher phase, and spin-orbit related phase effects. Later, fundamental aspects of decoherence are introduced. The chapter concludes with a discussion of conductance fluctuations in ballistic and diffusive mesoscopic samples.

Beyond the basic interference effects introduced in Chapter 14, further interesting interference phenomena exist in semiconductor nanostructures, the discussion of which requires more prior knowledge. This chapter discusses the Fano effect in nanostructure transport that has been found in a number of very different experiments. Furthermore, it discusses experiments that measure the transmission phase in addition to the transmission probability using interferometric arrangements. Finally, the chapter returns to the topic of decoherence, and introduces experiments aiming at controlled decoherence of quantum states. This topic requires knowledge of interference and the basics of decoherence, and incorporates ideas of shot noise, the Aharonov–Bohm effect, the quantum Hall effect, double quantum dot physics, and the theory of quantum measurement.

Quantum information processing is a modern research topic in which many different disciplines within and beyond physics interact. This chapter first makes contact with basic concepts of classical information theory, which is often not familiar to physicists. It then introduces Shannon's entropy and related entropic quantities, revisits the sampling theorem, discusses the relation between thermodynamics, measurement, and information theory, and looks into Landauer's principle. The chapter looks into the very basics of quantum information, the description of qubits, and operations of qubits. Finally, qubit implementations are discussed based on charge and spin qubits in quantum dots. Experimental results on single and two-qubit operations, and issues of decoherence are discussed.

This chapter is devoted to the physics of cavity quantum electrodynamics (CQED) cats. After a brief reminder about the Schrödinger cat problem in quantum optics, it describes how a single atom interacting with a field made of many photons can leave its quantum imprint on this field, bringing it into a superposition of states with distinct classical attributes. It describes the preparation and detection of these ‘Schrödinger cat’ states. It presents simple decoherence models, which account for their extreme fragility. It describes experimental studies of decoherence, which constitute direct explorations of the quantum-classical boundary. It discusses limitations to the size of these cat states and ways to protect them efficiently against decoherence. Finally, the chapter describes proposals to generate and study non-local cats, superpositions of field states delocalised in two cavities.

In quantum electrodynamics, the matter degrees of freedom are coupled to the radiation field through a local, gauge-invariant interaction density. Due to the linear structure of this coupling, the problem of constructing a complete formal representation of the reduced matter dynamics can be solved exactly if the electromagnetic radiation field is initially in a Gaussian state. This chapter combines field theoretical methods with superoperator and influence functional techniques to derive an exact, relativistic representation for the reduced density matrix of the matter degrees of freedom which completely describes the influence of the electromagnetic radiation field on the matter dynamics. Several applications are treated, such as the suppression of the quantum coherence of charged particles caused by the emission of bremsstrahlung and the decoherence of many-particle states.

This final chapter starts with a brief review of quantum-gravity phenomenology. It then focuses on an important conceptual issue – the relevance of quantum gravity for the general interpretation of quantum theory. A central part is devoted to the discussion of the quantum-to-classical transition, with decoherence as its crucial mechanism. It is shown that the quantum states used in cosmology can be interpreted in a sensible way. The chapter also contains a discussion of the arrow of time in the light of quantum cosmology and ends with a brief outlook and reflections.