Local observables for entanglement detection of depolarized states

We present an explicit construction of entanglement witnesses for depolarized states in an arbitrary finite dimension. For an infinite dimension, we generalize the construction to twin beams perturbed by Gaussian noises in the phase and in the amplitude of the field. We show that entanglement detection for all these families of states require only three local measurements. The explicit form of the corresponding set of local observables needed for an entanglement witness is derived.