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Effect of losses on multipartite entanglement from cascaded four-wave mixing processes

Multipartite entanglement is an important resource in quantum information. For its generation and manipulation, optical losses are inevitable experimental imperfections that cannot be ignored. In this paper, by using the positivity under partial transposition criterion, we theoretically characterize the effect of losses on two multipartite entanglement cases, tripartite entanglement and quadripartite entanglement, which are generated by cascaded four-wave mixing processes. The characterization of entanglement is made possible by calculating the smallest symplectic eigenvalues of the partially transposed covariance matrix. It is verified that when the power gains are smaller than 5, both the tripartite and the quadripartite entanglement can be maintained under the realistic experimental condition (less than 20% losses). In addition, we also study how the losses will affect the entanglement of subsystems in both cases. Our results pave the way for the experimental implementation of multipartite entanglement in cascaded four-wave mixing processes.