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From topological to quantum entanglement. (English) Zbl 1416.81170
Summary: 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.

81T45 Topological field theories in quantum mechanics
81P40 Quantum coherence, entanglement, quantum correlations
58J28 Eta-invariants, Chern-Simons invariants
83E30 String and superstring theories in gravitational theory
Full Text: DOI arXiv
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