From topological to quantum entanglement
- 144 Downloads
Entanglement is a special feature of the quantum world that reflects the existence of subtle, often non-local, correlations between local degrees of freedom. In topological theories such non-local correlations can be given a very intuitive interpretation: quantum entanglement of subsystems means that there are “strings” connecting them. More generally, an entangled state, or similarly, the density matrix of a mixed state, can be represented by cobordisms of topological spaces. Using a formal mathematical definition of TQFT we construct basic examples of entangled states and compute their von Neumann entropy.
KeywordsTopological Field Theories Chern-Simons Theories
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
- L.H. Kauffman and E. Mehrotra, Topological aspects of quantum entanglement, arXiv:1611.08047.
- M.F. Atiyah, The geometry and physics of knots, Cambridge University Press, Cambriddge U.K. (1990).Google Scholar
- P.K. Aravind, Borromean entanglement of the GHZ state, in Potentiality, entanglement and passion-at-a-distance, R.S. Cohen et al. eds., Kluwer, U.S.A. (1997).Google Scholar
- M. Khovanov and L.H. Robert, Foam evaluation and Kronheimer-Mrowka theories, arXiv:1808.09662.