${\ell }_1$-norm and entanglement in screening out braiding from Yang-Baxter equation associated with ${\mathbb{Z}}_3$ parafermion

Abstract

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 ${\mathbb{Z}}_3$ parafermion. The 2-qutrit entangled state $|\Psi (\theta )⟩$, generated by acting the localized unitary solution $\breve{R}(\theta )$ of YBE on 2-qutrit natural basis, achieves its maximal ${\ell }_1$-norm and maximal von Neumann entropy simultaneously at $\theta =\pi /3$. Meanwhile, at $\theta =\pi /3$, the solutions of YBE reduces braid matrices, which implies the role of ${\ell }_1$-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 $9\times 9$ localized braid representation in 4-qutrit tensor product space $({\mathbb{C}}^3{)}^{\otimes 4}$ are 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 $\breve{R}$-matrix.

arXiv comment6 pages, 1 figures

References in corpus (14)

• Quantifying Coherence
• Braiding Operators are Universal Quantum Gates
• Comparing Quantum Entanglement and Topological Entanglement
• Braiding transformation, entanglement swapping and Berry phase in entanglement space
• Quantum Computing with Parafermions
• Optical Simulation of Yang-Baxter Equation
• Metaplectic Anyons, Majorana Zero Modes, and their Computational Power
• Berry phase and quantum criticality in Yang--Baxter systems
• Skein Theory and Topological Quantum Registers: Braiding Matrices and Topological Entanglement Entropy of Non-Abelian Quantum Hall States
• Localization of unitary braid group representations
• Entanglement and Berry Phase in a $(3\times 3)-$dimensional Yang-Baxter system
• Factorized Three-body S-Matrix Restrained by Yang-Baxter Equation and Quantum Entanglements
• Exact Solution of a Yang-Baxter Spin-1/2 Chain Model and Quantum Entanglement
• Multipartite $d-$level GHZ bases associated with generalized braid matrices

Cited by in corpus (2)

• New series of multi-parametric solutions to GYBE: quantum gates and integrability
• New type of solutions of Yang-Baxter equations, quantum entanglement and related physical models