Quantum steering based on cascaded four-wave mixing processes

Abstract

Multipartite quantum steering is an important quantum resource and the basis of secure quantum communication network. Multipartite quantum steering can be generated by beam splitter networks, optical frequency comb systems and nonlinear processes. Different types of quantum steering will be produced by different projects. In this paper, we design two different schemes, i.e. series cascaded four-wave mixing and hybrid cascaded four-wave mixing, and based on these two schemes tripartite quantum steering and quinquepartite quantum steering are generated respectively. The steering characters among different users are quantified based on the covariance matrix. In theory, we investigate steering parameters among different modes created by two schemes versus the amplitude gain of four-wave mixing process. We find that one mode can steer the other two modes separately, but the other two modes cannot steer the one mode simultaneously. By comparing the steering characters of joint multimodes to a certain single mode with the individual mode to the single mode respectively, it can be seen that the steerability of the former is stronger than the latter in the whole gain region, and there exists only the steering of joint multimodes to a single mode in the partial gain region. More importantly, the steerability of joint multimodes to a single mode can be enhanced with the quantity of joint multimodes increasing. The results show that multiple types of quantum steering can be realized by using these two schemes, which are helpful in understanding the distribution of quantum steering in multipartite system and have important significance in practical secure quantum communication and quantum secret sharing.