arXiv:2212.13149v1 [math.RA] 26 Dec 2022

Also, in the single YBE situation, it was observed that the nilpotent coefficient matrix situation is the most interesting and important. A generalization of this for the system is the case, A,B are zero-divisors (i.e., AB = BA = 0). So, it makes ample sense to investigate the system of YBE when the coefficients satisfy AB = BA = 0.

Set-theoretical solutions to the Hom-Yang-Baxter

A solution to the Yang-Baxter equation (YBE shortly) is a linear map R: V ⊗ V → V ⊗ V such that (R ⊗ id V) (id V ⊗ R) (R ⊗ id V) = (id V ⊗ R) (R ⊗ id V) (id V ⊗ R). YBE first appeared in the work of Yang [39] and Baxter [1]. This equation is fundamental to quantum groups. It is a central task to determine all solutions to YBE ...

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Duality Quantum Simulation of the Yang-Baxter …

the YBE subsystem and an ancillary qubit. Thus, the entanglement between the two hand sides of the YBE or between two YBE systems with same dimensions can be investigated further. We will start with the duality quantum simulation of a reduced two-dimensional Yang-Baxter equation, and a general case of the YBE will also be investigated.

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THE BRAIDING MATRICES LINK BETWEEN YANG-BAXTER …

YBE. Unitary solutions pertaining to the comprehensive YBE at times further allow braid group depictions and consequently could be utilized for quantum information processing. An 8×8 answer to a comprehensive YBE is utilized to develop the Greenberger–Horne– Zeillinger states (Rowell et al., 2010). Answers to the YBE are hard to discover.

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