Genuine Quadripartite Continuous‐Variable Entanglement in Symmetric Cascaded Four‐Wave Mixing Process

Abstract

The symmetric cascaded four‐wave mixing process is a phase‐insensitive and easy‐to‐implement technology to prepare quadripartite entanglement. However, it has not yet been discussed whether the state generated by this method is genuinely entangled. Here, it is shown that the genuine quadripartite entanglement criteria previously derived are not applicable to the symmetric cascaded scheme. Thus some more effective sufficient conditions are derived for detecting genuine entanglement in this work. The existence of genuine quadripartite entanglement is then confirmed through different entanglement witnesses. Under the premise that the quadripartite state is genuinely entangled, the quantum gain of the first‐stage determines the optimal range of the quantum gain of second‐stage. Finally, it is show that the four output modes are genuinely entangled within the appropriate quantum gain ranges when the optical loss of each step of the cascaded system is less than 10%. The results pave the way for the experimental generation of genuine quadripartite entanglement in symmetric cascaded scheme.

Continuous variable multipartite entanglement in cascaded nonlinearities

“…Thus in order to resolve this anomalous behavior of modes â1 − â2 (and â3 − â4 ), we consider the necessary and sufficient DGCZ criterion for the bipartite system. We define the EPR-like quadrature operators as given in equations (17a) and (17b) and check the inequality (18) with these operators. As a result, we plot the normalized sum shown on the left-hand side of inequality (18) as a function of the gains G 1 and G 2 in figure 4, a value of this sum less than two proves the presence of entanglement.…”

“…We define the EPR-like quadrature operators as given in equations (17a) and (17b) and check the inequality (18) with these operators. As a result, we plot the normalized sum shown on the left-hand side of inequality (18) as a function of the gains G 1 and G 2 in figure 4, a value of this sum less than two proves the presence of entanglement. Now on comparing the results plotted in figure 4 with the corresponding results in figure 2, one can clearly see that there is a perfect corroboration between the presented results, which is as expected because both the DGCZ and Simon's negative partial transpose criterion provide a necessary and sufficient condition for bipartite entanglement detection.…”

Tunable Continuous‐Variable Tripartite Entanglement via Simultaneous and Ordinal Cascaded Nonlinear Processes

“…[37][38][39] The cascaded FWM process in rubidium vapor has also been experimentally demonstrated to be effective in generating multipartite entanglement. [40][41][42][43] In addition, in contrast to GHZ states generated based on a linear beam splitter network with a symmetric structure, Gaussian states can be generated by a cascaded nonlinear process with symmetric [43][44][45] or asymmetric [40,41] system. Inspired by previous works, in this paper, we consider simultaneous cascaded FWM (SC-FWM) and ordinal cascaded FWM (OC-FWM) schemes to generate triple-mode CV entanglement, and investigate the differences in their entanglement properties and mode structures.…”