Tripartite entanglement sudden death in Yang-Baxter systems

In this paper, we derive unitary Yang-Baxter $${\breve{R}(\theta, \varphi)}$$ matrices from the $${8\times8\,\mathbb{M}}$$ matrix and the 4 × 4 M matrix by Yang-Baxteration approach, where $${\mathbb{M}/M}$$ is the image of the braid group representation. In Yang-Baxter systems, we explore the evolution of tripartite negativity for three qubits Greenberger-Horne-Zeilinger (GHZ)-type states and W-type states and investigate the evolution of the bipartite concurrence for 2 qubits Bell-type states. We show that tripartite entanglement sudden death (ESD) and bipartite ESD all can happen in Yang-Baxter systems and find that ESD all are sensitive to the initial condition. Interestingly, we find that in the Yang-Baxter system, GHZ-type states can have bipartite entanglement and bipartite ESD, and find that in some initial conditions, W-type states have tripartite ESD while they have no bipartite Entanglement. It is worth noting that the meaningful parameter $${\varphi}$$ has great influence on bipartite ESD for two qubits Bell-type states in the Yang-Baxter system.

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