Related papers: Geometric information in eight dimensions vs. quan…
Recent work on state sum models of quantum gravity in 3 and 4 dimensions has led to interest in the `quantum tetrahedron'. Starting with a classical phase space whose points correspond to geometries of the tetrahedron in R^3, we use…
In this Thesis we examine the interplay between the encoding of information in quantum systems and their geometrical and topological properties. We first study photonic qubit probes of space-time curvature, showing how gauge-independent…
Graph-based collaborative filtering is capable of capturing the essential and abundant collaborative signals from the high-order interactions, and thus received increasingly research interests. Conventionally, the embeddings of users and…
The use of geometric and symmetry techniques in quantum and classical information processing has a long tradition across the physical sciences as a means of theoretical discovery and applied problem solving. In the modern era, the emergent…
This paper lays the foundations for a unified framework for numerically and computationally applying methods drawn from a range of currently distinct geometrical approaches to statistical modelling. In so doing, it extends information…
Geometric algebra was initiated by W.K. Clifford over 130 years ago. It unifies all branches of physics, and has found rich applications in robotics, signal processing, ray tracing, virtual reality, computer vision, vector field processing,…
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
Mathematical objects are generally abstract and not very approachable. Illustrations and interactive visualizations help both students and professionals to comprehend mathematical material and to work with it. This approach lends itself…
A model of joint random walk of two agents on an infinite plane is considered. The agents possess no means of mutual classical communication, but have access to quantum entanglement resource which is used according to a pre-arranged…
This document is meant as a pedagogical introduction to the modern language used to talk about quantum theory, especially in the field of quantum information. It assumes that the reader has taken a first traditional course on quantum…
At any point of a surface in the four-dimensional Euclidean space we consider the geometric configuration consisting of two figures: the tangent indicatrix, which is a conic in the tangent plane, and the normal curvature ellipse. We show…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…
We study a geometrical representation of the quantum information metric in the gauge/gravity correspondence. We consider the quantum information metric that measures the distance between the ground states of two theories on the field theory…
An analogy with real Clifford algebras on even-dimensional vector spaces suggests to assign a couple of space and time dimensions modulo 8 to any algebra (represented over a complex Hilbert space) containing two self-adjoint involutions and…
It is shown that the generators of Clifford algebras behave as creation and annihilation operators for fermions and bosons. They can create extended objects, such as strings and branes, and can induce curved metric of our spacetime. At a…
We study a differential geometric construction, the warped product, on the background geometry for information theory. Divergences, dual structures and symmetric 3-tensor are studied under this construction, and we show that warped product…
This note considers Kak's observer-reference model of quantum information, where it is shown that qubits carry information that is sqrt n / ln n times classical information, where n is the number of components in the measurement system, to…