Quantum Chromatic Numbers of Some Graphs in Hamming Schemes

Abstract:
In recent years, combinatorial designs and graph theory have become useful tools in the study of quantum communications and quantum information processing. For example, quantum states constructed from graphs and hypergraphs are used to study entanglement phenomena and construct high-performance quantum error correction codes; spherical designs are used to construct various types of unbiased bases for quantum measurement. In this talk, I will introduce some progress on quantum homomorphism of graphs. To be explicit, we have determined the quantum chromatic numbers of one class of Hamming graphs, and we also provide some bounds for the quantum chromatic numbers of some other graphs in Hamming schemes. We show that, for many Hamming graphs, their quantum chromatic numbers are strictly less than the classical chromatic numbers.


Biography:
Xiwang Cao received his education at Huanggang Normal University, Hubei University, and Peking University. He served as a Lecturer and later as an Associate Professor at Huanggang Normal University for 15 years. During this period, he obtained his master's degree from Hubei University and his PhD from Peking University. In 2004, he joined Nanjing University of Aeronautics and Astronautics, where he was promoted to Full Professor in 2007. Professor Cao’s research interests lie primarily in coding theory and combinatorics. He has published more than 150 papers in international journals and was awarded the Jiangsu Provincial Science and Technology Award in 2017. He has also been a visiting scholar at several prestigious institutions, including the Beijing International Centre for Mathematical Research (2010), the Institute of Mathematics at Academia Sinica (during the summers of 2014–2018), and Nanyang Technological University, Singapore (January 2018).