Related papers: From Information Geometry to Quantum Theory
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
Information geometry is concerned with the application of differential geometry concepts in the study of the parametric spaces of statistical models. When the random variables are independent and identically distributed, the underlying…
The uncertainty relation is a distinctive characteristic of quantum theory. The uncertainty is essentially rooted in quantum states. In this work we regard the uncertainty as an intrinsic property of quantum state and characterize it…
In this work we build a theoretical framework for the transport of information in quantum systems. This is a framework aimed at describing how out of equilibrium open quantum systems move information around their state space, using an…
The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarise not just quantum computing, but the whole subject of quantum information theory.…
In this work we: (1) review likelihood-based inference for parameter estimation and the construction of confidence regions; and, (2) explore the use of techniques from information geometry, including geodesic curves and Riemann scalar…
The aim of the present paper is twofold. First, to give the main ideas behind quantum computingand quantum information, a field based on quantum-mechanical phenomena. Therefore, a shortreview is devoted to (i) quantum bits or qubits (and…
A general noncommutative-geometric theory of principal bundles is presented. Quantum groups play the role of structure groups. General quantum spaces play the role of base manifolds. A differential calculus on quantum principal bundles is…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
This thesis investigates the connection between quantum theory, thermodynamics and information theory. Theories with structure similar to that of quantum theory are considered, mathematically described by the framework of "Generalized…
By virtue of the Noether theorems, the vast gauge redundancy of general relativity provides us with a rich algebra of boundary charges that generate physical symmetries. These charges are located at codimension-2 entangling surfaces called…
I review results from recent investigations of anomalies in fermion--Yang Mills systems in which basic notions from noncommutative geometry (NCG) where found to naturally appear. The general theme is that derivations of anomalies from…
This thesis consists of two parts. The first part is about how quantum theory can be recovered from first principles, while the second part is about the application of diagrammatic reasoning, specifically the ZX-calculus, to practical…
In recent years, diagrammatic languages have been shown to be a powerful and expressive tool for reasoning about physical, logical, and semantic processes represented as morphisms in a monoidal category. In particular, categorical quantum…
The black hole final state proposal implements manifest unitarity in the process of black hole formation and evaporation in quantum gravity, by postulating a unique final state boundary condition at the singularity. We argue that this…
Quantum theory and general relativity are about one century old. At present, they are considered the best available explanations of physical reality, and they have been so far corroborated by all experiments realised so far. Nonetheless,…
We reconstruct the explicit formalism of qubit quantum theory from elementary rules on an observer's information acquisition. Our approach is purely operational: we consider an observer O interrogating a system S with binary questions and…