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From Topological to Quantum Entanglement

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arxiv 1809.04574 v1 pith:SUBYUGWZ submitted 2018-09-12 hep-th quant-ph

D. Melnikov , A. Mironov , S. Mironov , A. Morozov , An. Morozov This is my paper
classification hep-thquant-ph
keywords entanglementquantumtopologicalcorrelationsentanglednon-localstatebasic
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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  1. Analyzing reduced density matrices in SU(2) Chern-Simons theory

    hep-th 2025-04 unverdicted novelty 4.0 of 10

    For p-party pure states from T_{p,p} torus link complements in SU(2)_k Chern-Simons theory, the characteristic polynomials of (1|p-1)-reduced density matrices are monic polynomials with rational coefficients.

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