From Topological to Quantum Entanglement
arXiv:1809.04574 · doi:10.1007/JHEP05(2019)116
Abstract
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.
arXiv comment9 pages
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Cited by in corpus (17)
- Circuit Complexity in Topological Quantum Field Theory
- Distinguishing Mutant Knots
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- TQFT gravity and ensemble holography
- Planar decomposition of the HOMFLY polynomial for bipartite knots and links
- Entanglement on multiple boundaries in Chern-Simons theory
- A new symmetry of the colored Alexander polynomial
- Entanglement Classification from a Topological Perspective
- Planar decomposition of bipartite HOMFLY polynomials in symmetric representations
- Multi-boundary entanglement in Chern-Simons theory with finite gauge groups
- Connectomes and Properties of Quantum Entanglement
- Topological entanglement and hyperbolic volume
- Polyadic braid operators and higher braiding gates
- Entanglement in Typical States of Chern-Simons Theory
- Multipartite Entanglement Structure of Fibered Link States
- Operator lift of Reshetikhin-Turaev formalism to Khovanov-Rozansky TQFTs
- Graph approach to quantum teleportation dynamics