相关论文: Axiomatic Quantum Theory
These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when -- as in quantum field…
In quantum field theory there is now a well developed technique, effective field theory, which allows one to obtain low energy quantum predictions in ``non-renormalizable'' theories, using only the degrees of freedom and interactions…
This paper proposes a general framework for nonperturbatively defining continuum quantum field theories. Unlike most such frameworks, the one offered here is finitary: continuum theories are defined by reducing large but finite quantum…
A modal logic based on quantum logic is formalized in its simplest possible form. Specifically, a relational semantics and a sequent calculus are provided, and the soundness and the completeness theorems connecting both notions are…
Quantum mechanics, information theory, and relativity theory are the basic foundations of theoretical physics. The acquisition of information from a quantum system is the interface of classical and quantum physics. Essential tools for its…
We stress the notion of statistical experiment, which is mandatory for quantum mechanics, and recall Ludwig's foundation of quantum mechanics, which provides the most general framework to deal with statistical experiments giving evidence…
The mathematical model of orthodox quantum mechanics has been critically examined and some deficiencies have been summarized. The model based on the extended Hilbert space and free of these shortages has been proposed; parameters being…
We derive the category-theoretic backbone of quantum theory from a process ontology. More specifically, we treat quantum theory as a theory of systems, processes and their interactions. In this first part of a three-part overview, we first…
Section headings: 1 Qubits, gates and networks 2 Quantum arithmetic and function evaluations 3 Algorithms and their complexity 4 From interferometers to computers 5 The first quantum algorithms 6 Quantum search 7 Optimal phase estimation 8…
This paper is a review of the theory of abelian anyons in planar systems at an introductory level and with focus on the formalism of quantum field theory, but with the aim of clarify the connections between the mathematical structure and…
Recent years have seen noteworthy progress in the mathematical formulation of quantum field theory and perturbative string theory. We give a brief survey of these developments. It serves as an introduction to the more detailed collection…
In this note, we survey some elementary theorems and proofs concerning dynamical matrices theory. Some mathematical concepts and results involved in quantum information theory are reviewed. A little new result on the matrix representation…
A brief summary of the physics of low-dimensional quantum systems is given. The material should be accessible to advanced physics undergraduate students. References to recent review articles and books are provided when possible.
After introducing the basic ingredients of Loop Quantum Cosmology, I will briefly discuss some of its phenomenological aspects. Those can give some useful insight about the full Loop Quantum Gravity theory and provide an answer to some…
Quantum cosmology has traditionally been studied at the level of symmetry-reduced minisuperspace models, analyzing the behavior of wave functions. However, in the absence of a complete full setting of quantum gravity and detailed knowledge…
This paper is an essentially self-contained and rigorous description of the fundamental principles of quantum computing from a mathematical perspective. It is intended to help mathematicians who want to get a grasp of this quickly growing…
A sketch is given of a circle of ideas relating quantum field theories with representation theory. The main mathematical ingredients are spinor geometry and the gauge group equivariant K-theory of the space of connections.
Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start…
This is an introduction to quantum algebra, from a geometric perspective. The classical spaces $X$, such as the Lie groups, homogeneous spaces, or more general manifolds, are described by various algebras $A$, defined over various fields…
We discuss foundation of quantum mechanics (interpretations, superposition, principle of complementarity, locality, hidden variables) and quantum information theory.