Related papers: A Tutorial on Knots and Quantum Mechanics
Knots are familiar entities that appear at a captivating nexus of art, technology, mathematics, and science. As topologically stable objects within field theories, they have been speculatively proposed as explanations for diverse persistent…
Loop quantum gravity has provided us with a canonical framework especially devised for background independent and diffeomorphism invariant gauge field theories. In this quantization the fundamental excitations are called spin network…
It is shown that quantum mechanics is a plausible statistical description of an ontology described by classical electrodynamics. The reason that no contradiction arises with various no-go theorems regarding the compatibility of QM with a…
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…
Classification of entanglement is an important problem in Quantum Resource Theory. In this paper we discuss an embedding of this problem in the context of Topological Quantum Field Theories (TQFT). This approach allows classifying…
Some of the basic concepts of topology are explored through known physics problems. This helps us in two ways, one, in motivating the definitions and the concepts, and two, in showing that topological analysis leads to a clearer…
The quantum mechanical formalism doesn't support our intuition, nor does it elucidate the key concepts that govern the behaviour of the entities that are subject to the laws of quantum physics. The arrays of complex numbers are kin to the…
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks…
We discuss the basic problem of signal transmission in quantum mechanics in terms of topological theories. Using the analogy between knot diagrams and quantum amplitudes we calculate the transmission coefficients of the concept topological…
Quantum networking is an emerging area with the potential to transform information processing and communications. In this paper, we present a brief introduction to quantum network control, an area in quantum networking dedicated to…
We survey indications from different branches of Physics that the fine scale structure of spacetime is not adequately described by a manifold. Based on the hints we accumulate, we propose a new structure, which we call a quantum topos. In…
We investigate quantum tomography in scenarios where prior information restricts the state space to a smooth manifold of lower dimensionality. By considering stability we provide a general framework that relates the topology of the manifold…
We provide a systematic approach to quantum mechanics from an information-theoretic perspective using the language of tensor networks. Our formulation needs only a single kind of object, so-called positive *-tensors. Physical models…
A knot theoretic algorithm is proposed to model `fragile topology' of quantum physics.
In topological quantum computation, quantum information is stored in states which are intrinsically protected from decoherence, and quantum gates are carried out by dragging particle-like excitations (quasiparticles) around one another in…
We present a general formalism with the aim of describing the situation of an entity, how it is, how it reacts to experiments, how we can make statistics with it, and how it changes under the influence of the rest of the universe. Therefore…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
We discuss the extension of loop quantum gravity to topspin networks, a proposal which allows topological information to be encoded in spin networks. We will show that this requires minimal changes to the phase space, C*-algebra and Hilbert…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
The theory of quantum thermodynamics investigates how the concepts of heat, work, and temperature can be carried over to the quantum realm, where fluctuations and randomness are fundamentally unavoidable. Of particular practical relevance…