# $$\ell _1$$-norm in three-qubit quantum entanglement constrained by Yang-Baxter equation

@article{Yu2020ell\_I,
title={$$\ell \_1$$-norm in three-qubit quantum entanglement constrained by Yang-Baxter equation},
author={Li-Wei Yu and Mo-Lin Ge},
journal={Quantum Inf. Process.},
year={2020},
volume={19},
pages={76}
}
• Published 3 February 2019
• Physics
• Quantum Inf. Process.
Usually the $\ell_2$-norm plays vital roles in quantum physics, acting as the probability of states. In this paper, we show the important roles of $\ell_1$-norm in Yang-Baxter quantum system, in connection with both the braid matrix and quantum entanglements. Concretely, we choose the 2-body and 3-body S-matrices, constrained by Yang-Baxter equation. It has been shown that for 2-body case, the extreme values of $\ell_1$-norm lead to two types of braid matrices and 2-qubit Bell states. Here we…

## References

SHOWING 1-10 OF 53 REFERENCES
Local unitary representation of braids and N-qubit entanglements
It is shown that the separability of varPsi \rangle = B|0⟩⊗N is closely related to the diagrammatic version of the braid operator $$\mathcal {B}$$B.
Yang–Baxter equations and quantum entanglements
• Physics
Quantum Inf. Process.
• 2016
The braiding matrix of Kauffman–Lomonaco has been extended to the solution (called type-II) of Yang–Baxter equation (YBE) and the related chain Hamiltonian is given.
The role of the ℓ1-norm in quantum information theory and two types of the Yang–Baxter equation
• Physics
• 2011
The role of the l1-norm in the Yang–Baxter system has been studied through Wigner's D-functions, where l1-norm means ∑i|Ci| for |Ψ = ∑iCi|ψi with |ψi being the orthonormal basis. It is shown that the
Non-Abelian Anyons and Topological Quantum Computation
• Physics
• 2008
Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of
Braiding transformation, entanglement swapping, and Berry phase in entanglement space
• Physics
• 2007
We show that braiding transformation is a natural approach to describe quantum entanglement by using the unitary braiding operators to realize entanglement swapping and generate the
Topological Quantum Computation
• Physics
• 2001
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones poly-
On Uncertainty, Braiding and Entanglement in Geometric Quantum Mechanics
• Physics
• 2006
Acting within the framework of geometric quantum mechanics, an interpretation of quantum uncertainty is discussed in terms of Jacobi fields, and a connection with the theory of elliptic curves is
Three qubits can be entangled in two inequivalent ways
• Physics
• 2000
Invertible local transformations of a multipartite system are used to define equivalence classes in the set of entangled states. This classification concerns the entanglement properties of a single
Universal quantum computation with the v=5/2 fractional quantum Hall state
We consider topological quantum computation (TQC) with a particular class of anyons that are believed to exist in the fractional quantum Hall effect state at Landau-level filling fraction v =5/2.