## I. INTRODUCTION 

It has been realized that quantum entanglement is a key ingredient in quantum compu- tation, quantum communication, and quantum cryptography[1]. Many two-level quantum systems, or qubits, have been widely used in quantum information[2, 3]. Recently, the bipar- tite qutrit systems have drawn people’s attention and exhibited varieties of advantages. It enables powerful computation[4], establishes secure communication[5] and cryptography[6], and reduces the communication complexity[7]. Additionally, the high energy quantum tele- portation using neutral kaons has been investigated[8]. These hint the possibility of con- necting quantum information and particle physics, this connection may reveal novel and interesting feature. Considering these two aspects, we take the mixed light pseudoscalar meson states, a type of bipartite qutrit system, into account. 

In particle physics, the study on mixed meson states[9] plays an important role and many works are devoted to this field[10–12], especially the study on η − η ′ mixed state, since it provides a unique opportunity for testing QCD [13] which is widely used in describing strong interaction. In the last decades, people have studied the mixing angle[14], the hadronic η - η ′ decay[15], η - η ′ mixing in radiative φ -meson decay[16], and so on. However, much work of particle physics has been done for testing the theory and experiment while hardly concerned with quantum information and the related algebra configuration, such as Yangians. As is known, the light pseudoscalar meson states in quark-flavor basis have su (3) symmetry[17]. It is important to expand the research on the symmetry of pseudoscalar meson states to Yangian Y ( su (3)). 

Yangian, as an algebra beyond the Lie algebra, is a powerful mathematical method for investigating the new symmetry of quantum systems which are nonlinear and integrable. Demonstrating and investigating whether simple physical systems possess Yangian is impor- tant and helpful for exploring physical systems via quantum algebra. People have found the Yangian symmetry in many physical models, such as Calogero-Sutherland model[18], the Hubbard model[19] and the Heisenberg model[20], etc. The realizations of Y ( sl (2))[21, 22] as the simplest one in Yangian algebra have been gained much attention. However, the Yangian related to the Lie algebra su (3), Y ( su (3)), which is closed to the light pseudoscalar meson states in particle physics, need to be investigated in more detail. Thus, much atten- tion is going to be payed in this paper to the application of Y ( su (3)) algebra in the meson 

