Preparation of free-travelling three-mode W-type entangled squeezed vacuum states

•Three-mode W-type entangled squeezed vacuum states in free-travelling optical fields are proposed.•In the case of the fluctuation of nonlinear phase factor between two modes, the fidelity is approach unity.•The scheme can be generated to prepare other N-mode W-type ESVSs by choosing the beam splitters with appropriate reflectivity.

A scheme is proposed to prepare W-type entangled squeezed vacuum states (ESVSs) via free-travelling optical fields with simple linear optical devices, photo detectors and cross-Kerr medium. We investigate the influence of an inexact nonlinear phase factor between two modes on the fidelity of the prepared three-mode W  -type ESVSs. By adjusting the appropriate reflectivity, the scheme can be extended to create 2n+12n+1-mode W-type ESVSs.