Tripartite continuous-variable entanglement of NOPA system**Projected supported by the National Natural Science Foundation of China (Grant No. 11504074) and the Science Fund from the State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Shanxi, China (Grant No. KF201601).

Abstract

We investigate the fundamental limits to the achievable tripartite continuous-variable (CV) entanglement criterion of a generalized V1 criterion. Our numerical simulation results show that the non-degenerate eigenvalues do effect the performances of the estimated minimum variances. From below the threshold to above the threshold, with the increase of the pump parameter, the tripartite CV entanglement gradually disappears. The different off-diagonal elements seriously distort the weights for entanglement. We can obtain a good tripartite CV entanglement by appropriately controlling the values of off-diagonal elements εij.