Quantum Knots

Abstract

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 of the Aravind Hypothesis for comparing quantum measurement with classical topological measurement. We propose a separate, network model for quantum evolution and measurement, where the background space is replaced by an evolving network. In this model there is an analog of the Aravind Hypothesis that promises to directly illuminate relationships between physics, topology and quantum knots.

17 pages, 13 figures, LaTeX document

References in corpus (4)

• Comparing Quantum Entanglement and Topological Entanglement
• Spin network quantum simulator
• Entanglement Criteria - Quantum and Topological
• Unitary Solutions to the Yang-Baxter Equation in Dimension Four

Cited by in corpus (10)

• Three-Hilbert-Space Formulation of Quantum Mechanics
• Teleportation, Braid Group and Temperley--Lieb Algebra
• Yang-Baxter operators need quantum entanglement to distinguish knots
• A 3-Stranded Quantum Algorithm for the Jones Polynomial
• Entanglement Classification from a Topological Perspective
• Quantizing Knots and Beyond
• Mosaic number of knots
• Upper bound on the total number of knot $n$-mosaics
• Planarizable Supersymmetric Quantum Toboggans
• Small knot mosaics and partition matrices