Direct measurement of the Wigner characteristic function of an arbitrary multi-mode entangled traveling field

We present a simple proposal to measure arbitrary multi-mode entangled traveling field state based on a Mach–Zehnder interferometer in theory. Our method directly yields the characteristic function of the Wigner function without a demanding data analysis and can be easily carried out by recent technological advances. Especially, it is a very effective reconstruction proposal for an entangled traveling field with a small number of modes from the experimental point of view. We demonstrate the scheme for the example of a two-mode squeezed vacuum state to illustrate how similar the reconstructed state is to the ideal one via controlling the values of phase shifts.