Emergence of Network Bifurcation Triggered by Entanglement

Xi Yong; Man-Hong Yung; Xue-Ke Song; Xun Gao; Angsheng Li

doi:10.22331/q-2019-06-03-147

Emergence of Network Bifurcation Triggered by Entanglement

Xi Yong^1,2,3, Man-Hong Yung^4,5,6,7, Xue-Ke Song^4,5,8, Xun Gao⁶, and Angsheng Li¹

¹State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, P. R. China
²University of Chinese Academy of Sciences, P. R. China
³Water Information Center, Ministry of Water Resources, Beijing 100053, P. R. China
⁴Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, P. R. China
⁵Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, P. R. China
⁶Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, P. R. China
⁷Central Research Institute, Huawei Technologies, Shenzhen 518129, P. R. China
⁸Department of Physics, Southeast University, Nanjing 211189, P. R. China

Published:	2019-06-03, volume 3, page 147
Eprint:	arXiv:1609.03299v3
Doi:	https://doi.org/10.22331/q-2019-06-03-147
Citation:	Quantum 3, 147 (2019).

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Abstract

In many non-linear systems, such as plasma oscillation, boson condensation, chemical reaction, and even predatory-prey oscillation, the coarse-grained dynamics are governed by an equation containing anti-symmetric transitions, known as the anti-symmetric Lotka-Volterra (ALV) equations. In this work, we prove the existence of a novel bifurcation mechanism for the ALV equations, where the equilibrium state can be drastically changed by flipping the stability of a pair of fixed points. As an application, we focus on the implications of the bifurcation mechanism for evolutionary networks; we found that the bifurcation point can be determined quantitatively by the microscopic quantum entanglement. The equilibrium state can be critically changed from one type of global demographic condensation to another state that supports global cooperation for homogeneous networks. In other words, our results indicate that there exist a class of many-body systems where the macroscopic properties are invariant with a certain amount of microscopic entanglement, but they can be changed abruptly once the entanglement exceeds a critical value. Furthermore, we provide numerical evidence showing that the emergence of bifurcation is robust against the change of the network topologies, and the critical values are in good agreement with our theoretical prediction. These results show that the bifurcation mechanism could be ubiquitous in many physical systems, in addition to evolutionary networks.

► BibTeX data

@article{Yong2019emergenceofnetwork,
  doi = {10.22331/q-2019-06-03-147},
  url = {https://doi.org/10.22331/q-2019-06-03-147},
  title = {Emergence of {N}etwork {B}ifurcation {T}riggered by {E}ntanglement},
  author = {Yong, Xi and Yung, Man-Hong and Song, Xue-Ke and Gao, Xun and Li, Angsheng},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {3},
  pages = {147},
  month = jun,
  year = {2019}
}

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