On the role of the local oscillator intensity in optical homodyne-like tomography

In a recent research (Olivares et al., 2019 [18]) we have demonstrated that a homodyne-like scheme, exploiting a "low-intensity" local oscillator, can be used to perform optical state tomography of both quantum and classical states of light. The reconstruction method directly uses the homodyne-like probability distribution retrieved from the detector. Here, we further investigate the role played by the local oscillator in this respect. In particular, we study to some extent how its intensity affects the quantum-state reconstruction procedure by focusing on the case of the Fock states |1? and |2?, whose homodyne-like probability distributions are sensibly affected by the actual value of the LO intensity. The analysis is performed on Monte Carlo simulated experiments taking also into account the quantum detection efficiency.