# Quantum entanglement, unitary braid representation and Temperley-Lieb algebra

@article{Ho2010QuantumEU, title={Quantum entanglement, unitary braid representation and Temperley-Lieb algebra}, author={C. L. Ho and Allan I. Solomon and C.H.Oh}, journal={EPL}, year={2010}, volume={92}, pages={30002} }

Important developments in fault-tolerant quantum computation using the braiding of anyons have placed the theory of braid groups at the very foundation of topological quantum computing. Furthermore, the realization by Kauffman and Lomonaco that a specific braiding operator from the solution of the Yang-Baxter equation, namely the Bell matrix, is universal implies that in principle all quantum gates can be constructed from braiding operators together with single qubit gates. In this paper we… Expand

#### 11 Citations

A note on "eight-vertex" universal quantum gates

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Abstract We present a formula for an infinite number of universal quantum logic gates, which are 4 by 4 unitary solutions to the Yang–Baxter (Y–B) equation. We obtain this family from a certain… Expand

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We study quantum information aspects of the fermionic entanglement negativity recently introduced in [Phys. Rev. B 95, 165101 (2017)] based on the fermionic partial transpose. In particular, we show… Expand

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New classes of spin chains from (SÔ(q)(N), Sp̂(q)(N)) Temperley-Lieb algebras: Data transmission and (q, N) parametrized entanglement entropies

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A Temperley-Lieb algebra is extracted from the operator structure of a new class of N2×N2 braid matrices presented and studied in previous papers and designated as SO(q)(N), Sp(q)(N) for the… Expand

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Abstract In this letter, we study the two-spin-1/2 realization for the Birman–Murakami–Wenzl (B–M–W) algebra and the corresponding Yang–Baxter R ˘ ( θ , ϕ ) matrix. Based on the two-spin-1/2… Expand

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We propose a scheme for classifying the entanglement of a tripartite pure qubit state. This classification scheme consists of an ordered list of seven elements. These elements are the Cayley… Expand

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