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Topological Quantum Computing Entanglement Theory Quantum Correlations

Yang-Baxter operators need quantum entanglement to distinguish knots

arXiv
Authors: Gorjan Alagic, Michael Jarret, Stephen P. Jordan

Year

2015

Paper ID

28007

Status

Preprint

Abstract Read

~2 min

Abstract Words

77

Citations

N/A

Abstract

Any solution to the Yang-Baxter equation yields a family of representations of braid groups. Under certain conditions, identified by Turaev, the appropriately normalized trace of these representations yields a link invariant. Any Yang-Baxter solution can be interpreted as a two-qudit quantum gate. Here we show that if this gate is non-entangling, then the resulting invariant of knots is trivial. We thus obtain a general connection between topological entanglement and quantum entanglement, as suggested by Kauffman et al.

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  • This paper contributes to the Topological Quantum Computing research area in the Quantum Articles archive.
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  • Any solution to the Yang-Baxter equation yields a family of representations of braid groups.

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