Quasiprobability functions measured by photon statistics of amplified signal fields

Abstract

A quantum state can be described by its quasiprobability functions or by its density matrix. The quasiprobability functions and density matrix for nonclassical fields have been measured by making use of homodyne detection schemes. We suggest direct photodetection of the amplified signal fields for the quasiprobability function measurements. Linear amplification is described in phase space by a convolution of the signal field to the idler field, which normally determines added noise during amplification. Taking the coherent idler field and using the convolution relation, we show that the direct photodetection of the amplified field results in a quasiprobability function for the signal field. In particular, the probability of there being no photons in the amplified field is the scaled $Q$ function for the signal field.