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The relationships between quantum entangled states and braid matrices have been well studied in recent years. However, most of the results are based on qubits. In this paper, we investigate the applications of 2-qutrit entanglement in the braiding associated with Z 3 parafermion. The 2-qutrit entangled state | Ψ ( θ ) 〉 , generated by the action of the localized unitary solution R ˘ ( θ ) of YBE on 2-qutrit natural basis, achieves its maximal ℓ 1 -norm and maximal von Neumann entropy simultaneously at θ = π / 3 . Meanwhile, at θ = π / 3 , the solutions of YBE reduces braid matrices, which implies the role of ℓ 1 -norm and entropy plays in determining real physical quantities. On the other hand, we give a new realization of 4-anyon topological basis by qutrit entangled states, then the 9 × 9 localized braid representation in 4-qutrit tensor product space ( C 3 ) ⊗ 4 is reduced to Jones representation of braiding in the 4-anyon topological basis. Hence, we conclude that the entangled states are powerful tools in analysing the characteristics of braiding and R ˘ -matrix. [ABSTRACT FROM AUTHOR]

The solutions of Yang-Baxter equation (YBE) associated with quantum information have been reviewed with new progress. The additivity rule for two particles is shown to obey Lorentzian type other than the Gallilean. Acting the braiding operations on the topological basis, it turns out that the -dimensional representations obeying YBE are nothing but the Wigner's -functions. The connection between the extremization of -norm as well as of von Neumann entropy and the reduction of YBE to braid relation is also discussed. [ABSTRACT FROM AUTHOR]

This paper investigates the physical effects of the Yang-Baxter equation (YBE) to quantum entanglements through the 3-body S-matrix in entangling parameter space. The explicit form of 3-body S-matrix R ̆ 123 (θ, φ) based on the 2-body S-matrices is given due to the factorization condition of YBE. The corresponding chain Hamiltonian has been obtained and diagonalized, also the Berry phase for 3-body system is given. It turns out that by choosing different spectral parameters the R ̆ (θ, φ) -matrix gives GHZ and W states respectively. The extended 1-D Kitaev toy model has been derived. Examples of the role of the model in entanglement transfer are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we review some results obtained in our works with extension. The new type of braiding matrices called type-II has been extended to the solutions of Yang-Baxter equations (YBE). It is related to quantum entangling states. The four-dimensional realization is connected with Majorana fermions and the two-dimensional realization for the topological basis is the wigner DJ-function with J = 1/2. The YBE leads to the conclusion that the additivity rule of velocities for two anyons obeys Lorentz rather than Galilean. The discussion is extended to three body S-matrix formed by three two-body S-matrices. The three-qubit entanglement based on two-qubit entanglements is discussed. [ABSTRACT FROM AUTHOR]

A new realization of doubling degeneracy based on emergent Majorana operator Γ presented by Lee-Wilczek has been made. The Hamiltonian can be obtained through the new type of solution of Yang-Baxter equation, i.e. -matrix. For 2-body interaction, gives the 'superconducting' chain that is the same as 1D Kitaev chain model. The 3-body Hamiltonian commuting with Γ is derived by 3-body -matrix, we thus show that the essence of the doubling degeneracy is due to . We also show that the extended Γ′-operator is an invariant of braid group BN for odd N. Moreover, with the extended Γ′-operator, we construct the high dimensional matrix representation of solution to Yang-Baxter equation and find its application in constructing 2N-qubit Greenberger-Horne-Zeilinger state for odd N. [ABSTRACT FROM AUTHOR]