Abstract
A method is introduced that allows one to measure normal-ordered moments of the displaced photon-number operator up to higher orders, without the need of photon-number resolving detectors. It is based on unbalanced homodyne correlation measurements, with the local oscillator being replaced by a displaced dephased laser. The measured moments yield a simple approximation of quasiprobabilities, representing the full quantum state. Quantum properties of light are efficiently certified through normal-ordered observables directly accessible by our method, which is illustrated for a weakly squeezed vacuum and a single-photon-added thermal state.
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