Local Unitary Representation of Braids and N-Qubit Entanglements

2017/06/05 by Yu, Li-Wei · 1 citation
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1706.01225

Abstract

In this paper, by utilizing the idea of stabilizer codes, we give some relationships between one local unitary representation of braid group in N-qubit tensor space and the corresponding entanglement properties of the N-qubit pure state |Ψ⟩, where the N-qubit state |Ψ⟩ is obtained by applying the braiding operation on the natural basis. Specifically, we show that the separability of |Ψ⟩=B|0⟩^{⊗ N} is closely related to the diagrammatic version of the braid operator B. This may provide us more insights about the topological entanglement and quantum entanglement.

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