Yang–Baxter equations and quantum entanglements

Durgun Duran

Hengyan Wang, Shijie Wei, Chao Zheng +6 more

The Yang-Baxter equation (YBE) has created many applications in the integrable models of the statistical mechanics. It is recently shown that the YBE can be further applied in quantum information processing. Conversely, quantum simulation also provides novel approaches for effectively checking the YBE in quantum devices. Here, we adopted the method inspired by the previous work to experimentally perform the simulation of the YBE on a four-qubit nuclear magnetic resonance quantum processor. Whether the YBE is satisfied or not can be preliminarily determined by measuring the ancillary qubit without the assistance of quantum state tomography, and two hand sides of the YBE are concurrently simulated, not in separate forms involved in the existing protocols. The experimental result shows that the discrimination accuracy is over 98.1% when the condition of YBE is satisfied. The global and local entanglements in the YBE system are also studied by the numerical simulation and experiments. It is found that the YBE is not only a tool to yield the global entanglement but also the symptom when the local entanglement is equal to each other.

Mo‐Lin Ge, Kang Xue

Mo‐Lin Ge

Mostafa Mansour

Recent study suggests that there are natural connections between quantum entanglement and the quantumYang-Baxter equation. The present paper introduce the unitary solutions of the Quantum Yang{Baxter Equationderived via the quantization-deformation of a Poisson Lie group associated to an r-matrix (solution of a classicalYang-Baxter equation). The solution of the algebraic Quantum Yang Baxter equation that we explore containa deformation parameter h, and will be used to performs quantum entanglement when acting on (multi)-qubitquantum states.

Gorjan Alagic, Michael Jarret, Stephen P. Jordan

Any solution to the Yang-Baxter equation yields a family of representations of braid groups. Under certain conditions, identified by Turaev, the appropriately normalized trace of these representations yields a link invariant. Any Yang-Baxter solution can be interpreted as a two-qudit quantum gate. Here we show that if this gate is non-entangling, then the resulting invariant of knots is trivial. We thus obtain a general connection between topological entanglement and quantum entanglement, as suggested by Kauffman et al.