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2 Generalized Quantum Theory: Overview and Latest Developments

Thomas Filk A

Published Aug 16, 2016• 41 citations
OpenAlex

Abstract

The main formal structures of Generalized Quantum Theory are summarized. Recent progress has sharpened some of the concepts, in particular the notion of an observable, the action of an observable on states (putting more emphasis on the role of proposition observables), and the concept of generalized entanglement. Furthermore, the active role of the observer in the structure of observables and the partitioning of systems is emphasized.

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The main formal structures of Generalized Quantum Theory are summarized. Recent progress has sharpened some of the concepts, in particular the notion of an observable, the action of an observable on states (putting more emphasis on the role of proposition observables), and the concept of generalized entanglement. Furthermore, the active role of the observer in the structure of observables and the partitioning of systems is emphasized.
Entanglement plays a pervasive role nowadays throughout quantum information science, and at the same time provides a bridging notion between quantum information science and fields as diverse as condensed-matter theory, quantum gravity, and quantum foundations. In recent years, a notion of ''Generalized Entanglement'' (GE) has emerged, based on the idea that entanglement may be directly defined through expectation values of preferred observables -- without reference to a preferred subsystem decomposition. Preferred observables capture the physically relevant point of view, as defined by dynamical, operational, or fundamental constraints. While reducing to the standard entanglement notion when preferred observables are restricted to arbitrary local observables acting on individual subsystems, GE substantially expands subsystem-based entanglement theories, in terms of both conceptual foundations and range of applicability. Remarkably, the GE framework allows for non-trivial entanglement to exist within a single, indecomposable quantum system, demands in general a distinction between quantum separability and absence of entanglement, and naturally extends to situations where existing approaches may not be directly useful -- such as entanglement in arbitrary convex-cones settings and entanglement for indistinguishable quantum particles. In this paper, we revisit the main motivations leading to GE, and summarize the accomplishments and prospects of the GE program to date, with an eye toward conceptual developments and implications. In particular, we explain how the GE approach both shares strong points of contact with abstract operational quantum theories and, ultimately, calls for an observer-dependent redefinition of concepts like locality, completeness, and reality in quantum theory.
Inferring causal relations from empirical data is a central task in any scientific inquiry. To that aim, a mathematical theory of causality has been developed, not only stating under which conditions such inference becomes possible but also offering a formal framework to reason about cause and effect within quantum theory. This perspective article provides an overview of the latest results in the growing field of quantum causality, with a special focus on experimental implementations and concepts that only recently have entered in the quantum information dictionary. Ideas like bilocality, instrumental variables and interventions will be discussed from both a fundamental and an experimental perspective.
Substantial progress has been achieved in the last couple of decades in computing the electronic structure of correlated materials from first principles. This progress has been driven by parallel development in theory and numerical algorithms. Theoretical development in combining ab initio approaches and many-body methods is particularly promising. A crucial role is also played by a systematic method for deriving a low-energy model, which bridges the gap between real and model systems. In this article, an overview is given tracing the development from the LDA+U to the latest progress in combining the G W method and (extended) dynamical mean-field theory ( G W +EDMFT). The emphasis is on conceptual and theoretical aspects rather than technical ones.
Beginning with the definition of a duplicated experiment and the fact that the resulting data are summarized as a set of configurations of some observables, together with frequencies of occurrence of each configuration, we derive the formal structure of conventional quantum theory using only the statistical properties of such data, and show that certain elements of the theory have heretofore been overlooked. This derivation yields a rather broad generalization of the theory which suggests new methods for describing phase transitions and possibly fundamental particles as well.