Related papers: FAPP and Non-FAPP
In this survey article we give basic introduction to the theory of quantum families of maps. We begin with a general look at non-commutative (or "quantum") topology. Then we formulate all our results in this language. Existence of quantum…
In order to support students in the development of expertise in quantum mechanics, we asked which concepts and structures can act as organizing principles of the non-relativistic theory. The research question has been addressed in a…
This report explains the basic theory and common terminology of quantum physics without assuming any knowledge of physics. It was written by a group of applied mathematicians while they were reading up on the subject. The intended audience…
The aim of this review is to provide a detailed account of the physical content emerging from this story of the canonical approach to Quantum Gravity. All the crucial steps in our presentation have a pedagogical character, providing the…
We discuss the motivation for pursuing research on the foundations of quantum theory.
A non-classical, non-quantum theory, or NCQ, is any fully consistent theory that differs fundamentally from both the corresponding classical and quantum theories, while exhibiting certain features common to both. Such theories are of…
Some explanations and implications of the underlying theory approach for quantum theories (QM or QFT) are discussed and suggested. This simple idea seems to have significantly nontrivial effects for our understanding of the quantum…
This is a series of lecture notes explaining topos theory and its application in physics.
I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of quantum information is to be understood as…
In this paper we give a self contained introduction to the conceptional and mathematical foundations of quantum information theory. In the first part we introduce the basic notions like entanglement, channels, teleportation etc. and their…
There are many falsely intuitive introductions to quantum theory and quantum computation in a handwave. There are also numerous documents which teach those subjects in a mathematically sound manner. To my knowledge this paper is the…
We present a conceptually clear introduction to quantum theory, deriving the theory from scratch from the point of view of quantum information. Different subsets of these lectures were taught to a wide variety of audiences, including…
In this conceptual paper, we discuss quantum formalisms which do not use the famous Axiom of Choice. We also consider the fundamental problem which addresses the (in)correctness of having the complex numbers as the base field for Hilbert…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
Recent measures of nonclassical correlations are motivated by different notions of classicality and operational means. Quantum discord has received a great deal of attention in studies involving quantum computation, metrology, dynamics,…
A rough overview is given over the most essential structures underlying all working quantum theoretical models as well as axiomatic and algebraic quantum field theory .
We discuss foundation of quantum mechanics (interpretations, superposition, principle of complementarity, locality, hidden variables) and quantum information theory.
This series of introductory lectures consists of two parts. In the first part, I rapidly review the basic notions of quantum physics and many primitives of quantum information (i.e. notions that one must be somehow familiar with in the…
This is a graduate course on elementary quantum mechanics written for the benefit of undergraduate and graduate students. It is the English version of physics/0003106, which I did at the suggestion of several students from different…
Nonclassical states of light and their correlations lie at the heart of quantum optics, serving as fundamental resources that underpin both the exploration of quantum phenomena and the realisation of quantum information protocols. These…