Yang-Baxter Equation and Quantum Information

Mo‐Lin Ge, Li-Wei Yu, Kang Xue +1 more

Mo‐Lin Ge, Kang Xue

Li-Wei Yu, Kang Xue, Mo‐Lin Ge

The solutions of Yang–Baxter equation (YBE) associated with quantum information have been reviewed with new progress. The additivity rule for two particles is shown to obey Lorentzian type other than the Gallilean. Acting the braiding operations on the topological basis, it turns out that the [Formula: see text]-dimensional representations obeying YBE are nothing but the Wigner’s [Formula: see text]-functions. The connection between the extremization of [Formula: see text]-norm as well as of von Neumann entropy and the reduction of YBE to braid relation is also discussed.

F. Anvari Vind, Angela Foerster, I. S. Oliveira +4 more

The Yang-Baxter equation is an important tool in theoretical physics, with many applications in different domains that span from condensed matter to string theory. Recently, the interest on the equation has increased due to its connection to quantum information processing. It has been shown that the Yang-Baxter equation is closely related to quantum entanglement and quantum computation. Therefore, owing to the broad relevance of this equation, besides theoretical studies, it also became significant to pursue its experimental implementation. Here, we show an experimental realization of the Yang-Baxter equation and verify its validity through a Nuclear Magnetic Resonance (NMR) interferometric setup. Our experiment was performed on a liquid state Iodotrifluoroethylene sample which contains molecules with three qubits. We use Controlled-transfer gates that allow us to build a pseudo-pure state from which we are able to apply a quantum information protocol that implements the Yang-Baxter equation.

Mo‐Lin Ge, Kang Xue

Vind, Fatemeh Anvari, Angela Foerster, Oliveira, Ivan S. +4 more

The Yang-Baxter equation is an important tool in theoretical physics, with many applications in different domains that span from condensed matter to string theory. Recently, the interest on the equation has increased due to its connection to quantum information processing. It has been shown that the Yang-Baxter equation is closely related to quantum entanglement and quantum computation. Therefore, owing to the broad relevance of this equation, besides theoretical studies, it also became significant to pursue its experimental implementation. Here, we show an experimental realization of the Yang-Baxter equation and verify its validity through a Nuclear Magnetic Resonance (NMR) interferometric setup. Our experiment was performed on a liquid state Iodotrifluoroethylene sample which contains molecules with three qubits. We use Controlled-transfer gates that allow us to build a pseudo-pure state from which we are able to apply a quantum information protocol that implements the Yang-Baxter equation.