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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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