as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal ''Schrodinger-cat states.'' The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation. Only the preferred pointer observable of the apparatus can store information that has predictive power. When the measured quantum system is microscopic and isolated, this restriction on the predictive utility of its correlations with the macroscopic apparatus results in the effective ''collapse of the wave packet.'' The existential interpretation implied by einselection regards observers as open quantum systems, distinguished only by their ability to acquire, store, and process information. Spreading of the correlations with the effectively classical pointer states throughout the environment allows one to understand ''classical reality'' as a property based on the relatively objective existence of the einselected states. Effectively classical pointer states can be ''found out'' without being re-prepared, e.g, by intercepting the information already present in the environment. The redundancy of the records of pointer states in the environment (which can be thought of as their ''fitness'' in the Darwinian sense) is a measure of their classicality. A new symmetry appears in this setting. Environment-assisted invariance or envariance sheds new light on the nature of ignorance of the state of the system due to quantum correlations with the environment and leads to Born's rules and to reduced density matrices, ultimately justifying basic principles of the program of decoherence and einselection.

/pdf/decoherence-einselection-and-the-quantum-origins-of-the-5c70dshgfi.pdf

Decoherence, einselection, and the quantum origins of the classical

We propose a realizable architecture using one-dimensional transmission line resonators to reach the strong-coupling limit of cavity quantum electrodynamics in superconducting electrical circuits. The vacuum Rabi frequency for the coupling of cavity photons to quantized excitations of an adjacent electrical circuit (qubit) can easily exceed the damping rates of both the cavity and qubit. This architecture is attractive both as a macroscopic analog of atomic physics experiments and for quantum computing and control, since it provides strong inhibition of spontaneous emission, potentially leading to greatly enhanced qubit lifetimes, allows high-fidelity quantum nondemolition measurements of the state of multiple qubits, and has a natural mechanism for entanglement of qubits separated by centimeter distances. In addition it would allow production of microwave photon states of fundamental importance for quantum communication.

https://arxiv.org/pdf/cond-mat/0402216.pdf

Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation

Information Theory and Reliable Communication

The task of quantizing general relativity raises serious questions about the meaning of the present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as the space-time geometry itself. This paper seeks to clarify the foundations of quantum mechanics. It presents a reformulation of quantum theory in a form believed suitable for application to general relativity. The aim is not to deny or contradict the conventional formulation of quantum theory, which has demonstrated its usefulness in an overwhelming variety of problems, but rather to supply a new, more general and complete formulation, from which the conventional interpretation can be deduced. The relationship of this new formulation to the older formulation is therefore that of a metatheory to a theory, that is, it is an underlying theory in which the nature and consistency, as well as the realm of applicability, of the older theory can be investigated and clarified.

"relative State" Formulation of Quantum Mechanics

Foundations Of Statistics

In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper, we show that, despite being prescribed by a fundamental law, probabilities for individual quantum systems can be understood within the Bayesian approach. We argue that the distinction between classical and quantum probabilities lies not in their definition, but in the nature of the information they encode. In the classical world, maximal information about a physical system is complete in the sense of providing definite answers for all possible questions that can be asked of the system. In the quantum world, maximal information is not complete and cannot be completed. Using this distinction, we show that any Bayesian probability assignment in quantum mechanics must have the form of the quantum probability rule, that maximal information about a quantum system leads to a unique quantum-state assignment, and that quantum theory provides a stronger connection between probability and measured frequency than can be justified classically. Finally, we give a Bayesian formulation of quantum-state tomography.

https://arxiv.org/pdf/quant-ph/0106133.pdf

Quantum probabilities as Bayesian probabilities

We present an elementary proof of the quantum de Finetti representation theorem, a quantum analog of de Finetti’s classical theorem on exchangeable probability assignments. This contrasts with the original proof of Hudson and Moody [Z. Wahrschein. verw. Geb. 33, 343 (1976)], which relies on advanced mathematics and does not share the same potential for generalization. The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. The quantum de Finetti theorem, in a closely analogous fashion, deals with exchangeable density-operator assignments and provides an operational definition of the concept of an “unknown quantum state” in quantum-state tomography. This result is especially important for information-based interpretations of quantum mechanics, where quantum states, like probabilities, are taken to be states of knowledge rather than...

Unknown Quantum States: The Quantum de Finetti Representation

We give an introduction to the QBist interpretation of quantum mechanics, which removes the paradoxes, conundra, and pseudo-problems that have plagued quantum foundations for the past nine decades. As an example, we show in detail how this interpretation eliminates “quantum nonlocality.”

http://reality2015.sciencesconf.org/conference/reality2015/pages/Quantum_mechanics_Fuchs_et_al.pdf

An introduction to QBism with an application to the locality of quantum mechanics

In the quantum-Bayesian interpretation of quantum theory (or QBism), the Born rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state. But if not, what is the role of the rule? In this paper, the argument is given that it should be seen as an empirical addition to Bayesian reasoning itself. Particularly, it is shown how to view the Born rule as a normative rule in addition to usual Dutch-book coherence. It is a rule that takes into account how one should assign probabilities to the consequences of various intended measurements on a physical system, but explicitly in terms of prior probabilities for and conditional probabilities consequent upon the imagined outcomes of a special counterfactual reference measurement. This interpretation is exemplified by representing quantum states in terms of probabilities for the outcomes of a fixed, fiducial symmetric informationally complete measurement. The extent to which the general form of the new normative rule implies the full state-space structure of quantum mechanics is explored.

Quantum-Bayesian coherence

The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. In this paper, we motivate and review two results that generalize de Finetti's theorem to the quantum mechanical setting: Namely a de Finetti theorem for quantum states and a de Finetti theorem for quantum operations. The quantum-state theorem, in a closely analogous fashion to the original de Finetti theorem, deals with exchangeable density-operator assignments and provides an operational definition of the concept of an "unknown quantum state" in quantum-state tomography. Similarly, the quantum-operation theorem gives an operational definition of an "unknown quantum operation" in quantum-process tomography. These results are especially important for a Bayesian interpretation of quantum mechanics, where quantum states and (at least some) quantum operations are taken to be states of belief rather than states of nature.

https://arxiv.org/pdf/quant-ph/0404156.pdf

Ruediger Schack

Papers

Quantum probabilities as Bayesian probabilities

Unknown Quantum States: The Quantum de Finetti Representation

An introduction to QBism with an application to the locality of quantum mechanics

Quantum-Bayesian coherence

Unknown Quantum States and Operations, a Bayesian View