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the fourth port of the hybrid ring. Since we assume full knowledge of V , an obvious choice is the vacuum or, as in this work, a weak thermal state. Vacuum or thermal states at gigahertz frequencies can be prepared reliably in an experiment by controlling the temperature [20, 21]. In the next step, we compute suitable correlations of the form 〈 C ℓ $_{1}$C m 2 〉 , where ℓ, m ∈ N$_{0}$ and the brackets denote ensemble averaging. In contrast to Hanbury Brown and Twiss experiments based on intensity (power) correlations [20], our method is devoted to the correlations of field quadratures (voltages). For the first signal moment, the mean values 〈 χ$_{1}$ 〉 and 〈 χ$_{2}$ 〉 vanish and one obtains 〈 S 〉 = 〈 C$_{1}$ 〉 /G = −〈 C$_{2}$ 〉 /G . All higher moments of signal and noise can now be calculated by induction: 

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