The single-particle spectral function of 56Ni has been computed within the framework of self-consistent Greens functions theory. The Faddeev random phase approximation method and the G-matrix technique are used to account for the effects of long- and short-range physics on the spectral distribution. Large scale calculations have been performed in spaces including up to ten oscillator shells. The chiral N3LO interaction is used together with a monopole correction that accounts for eventual missing three-nucleon forces. The single-particle energies associated with nucleon transfer to valence 1p0f orbits are found to be almost converged with respect to both the size of the model space and the oscillator frequency. The results support that 56Ni is a good doubly magic nucleus. The absolute spectroscopic factors to the valence states on A=55,57 are also obtained. For the transition between the ground states of 57Ni and 56Ni, the calculations nicely agree with heavy-ion knockout experiments.