Related papers: A Tutorial on Knots and Quantum Mechanics
We construct a topological space to study contextuality in quantum mechanics. The resulting space is a classifying space in the sense of algebraic topology. Cohomological invariants of our space correspond to physical quantities relevant to…
This paper discusses relationships between topological entanglement and quantum entanglement. Specifically, we propose that for this comparison it is fundamental to view topological entanglements such as braids as "entanglement operators"…
Quantum entanglement is a captivating phenomenon in quantum physics, characterized by intricate and non-classical correlations between particles. This phenomenon plays a crucial role in quantum computing and measurement processes. In this…
Encoding and manipulation of quantum information by means of topological degrees of freedom provides a promising way to achieve natural fault-tolerance that is built-in at the physical level. We show that this topological approach to…
This paper introduces a formalism that aims to describe the intricacies of quantum computation by establishing a connection with the mathematical foundations of tensor theory and multilinear maps. The focus is on providing a comprehensive…
In this paper we present the novel qualities of entanglement of formation for general (so also infinite dimensional) quantum systems and we introduce the notion of coefficient of quantum correlations. Our presentation stems from rigorous…
One of the most striking features of quantum phases that exhibit topological order is the presence of long range entanglement that cannot be detected by any local order parameter. The formalism of projected entangled-pair states is a…
We consider the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic…
Topology forms a cornerstone in modern condensed matter and statistical physics, offering a new framework to classify the phases and phase transitions beyond the traditional Landau paradigm. However, it is widely believed that topological…
A physical theory consists of the mathematical formalism and an interpretation, which contains the definition of symbols, measurement assignments, concepts and principles, and an ontology. We present a scheme to classify these different…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
We explain why, in a configuration space that is multiply connected, i.e., whose fundamental group is nontrivial, there are several quantum theories, corresponding to different choices of topological factors. We do this in the context of…
This paper proposes the definition of a quantum knot as a linear superposition of classical knots in three dimensional space. The definition is constructed and examples are discussed. Then the paper details extensions and also limitations…
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…
Harnessing the potential computational advantage of quantum computers for machine learning tasks relies on the uploading of classical data onto quantum computers through what are commonly referred to as quantum encodings. The choice of such…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
This is a series of lecture notes explaining topos theory and its application in physics.
I present some general ideas about quantum entanglement in relativistic quantum field theory, especially entanglement in the physical vacuum. Here, entanglement is defined between different single particle states (or modes), parameterized…
Quantum networks are composed of nodes which can send and receive quantum states by exchanging photons. Their goal is to facilitate quantum communication between any nodes, something which can be used to send secret messages in a secure…
Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…