Optical Simulation of Yang-Baxter Equation

Abstract

In this paper, several proposals of optically simulating Yang-Baxter equations have been presented. Motivated by the recent development of anyon theory, we apply Temperley-Lieb algebra as a bridge to recast four-dimentional Yang-Baxter equation into its two-dimensional counterpart. In accordance with both representations, we find the corresponding linear-optical simulations, based on the highly efficient optical elements. Both the freedom degrees of photon polarization and location are utilized as the qubit basis, in which the unitary Yang-Baxter matrices are decomposed into combination of actions of basic optical elements.

15 pages, 7 figures; introduction and second section are dramatically rewritten, in order to improve the physical sense

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Cited by in corpus (17)

• Yang-Baxter integrable models in experiments: from condensed matter to ultracold atoms
• Experimental realization of the Yang-Baxter Equation via NMR interferometry
• Direct Experimental Simulation of the Yang-Baxter Equation
• Temperley-Lieb Algebra, Yang-Baxterization and Universal Gate
• All Pure Two-Qudit Entangled States Can be Generated via a Universal Yang--Baxter Matrix Assisted by Local Unitary Transformations
• Factorized Three-body S-Matrix Restrained by Yang-Baxter Equation and Quantum Entanglements
• Optimal realization of Yang-Baxter gate on quantum computers
• Multipartite $d-$level GHZ bases associated with generalized braid matrices
• Topological Basis Associated with B-M-W algebra: Two Spin-1/2 Realization
• Berry phase and entanglement of 3 qubits in a new Yang-Baxter system
• Action in Hamiltonian Models Constructed by Yang-Baxter Equation: Entanglement and Measures of Correlation
• ${\ell }_1$-norm and entanglement in screening out braiding from Yang-Baxter equation associated with ${\mathbb{Z}}_3$ parafermion
• Birman-Wenzl-Murakami Algebra and the Topological Basis
• The Yang-Baxter equation, Quantum computing and Quantum entanglement
• A study on the relations between the topological parameter and entanglement
• Birman-Wenzl-Murakami Algebra, Topological parameter and Berry phase
• More about the doubling degeneracy operators associated with Majorana fermions and Yang-Baxter equation