On Feb. 26, a research team from the School of Mathematical Sciences and Carbon Neutral Development Institute of Jiangsu University (JSU) published a research paper titled “Unveiling the importance of nonshortest paths in quantum networks” in the journal of Science Advances. JSU was credited as the leading institution for the research. Prof. Dong Gaogao is the first corresponding author, while Hu Xinqi, his doctoral student from School of Mathematical Sciences, is the first author. The co-corresponding authors includes Prof. Meng Xiangyi from Rensselaer Polytechnic Institute, Prof. Kim Christensen from Imperial College London and Prof. Renaud Lambiotte from Oxford University. Additionally, Prof. Fan Jingfang from Beijing Normal University and Prof. Gao Jianxi from Rensselaer Polytechnic Institute, etc contributed as the co-authors.
From the perspective of complex network connectivity and based on the concurrent measurement of quantum entanglement, this study reveals the first principle of quantum network design from the aspects of theoretical analysis, numerical simulation and practical verification: Differing from the dependence on shortest paths of the transmission of electromagnetic wave information, nonshortest paths also play a very important role in quantum information transmission.
This work put forward a kind of statistical theoretical framework of quantum giant connectivity component, and applied it on a class of hierarchical scale-free network. Further analyzed are three critical exponents υ, β, df at the critical point of information transmission, to respectively characterize the divergence behavior of correlation length on finite scale networks, the rate that the network system forms a maximum connectivity, and the network spatial expansion efficiency of connectivity components.
The research found that for the proposed network topology structure, the critical exponents of quantum concurrence percolation and classical percolation satisfy the same hyper-scaling relationship but belong to diverse universality classes, which is different from regular lattice networks. Based on that, the team gives corresponding functional relationships and contribution degrees of the nonshortest path length to critical exponents in quantum networks. The results show that, different from classical percolation, the critical behaviors of quantum concurrence percolation always maintain non-negligible dependence on nonshortest paths. In addition, it is verified that the conclusion above also applies to real-world networks like Internet.
