Besides describing quantum dynamics, one can naturally apply the cluster-expansion approach to represent the quantum distributions. One possibility is to represent the quantum fluctuations of a quantized light mode B ^ ^ in terms of clusters, yielding the cluster-expansion representation. Alternatively, one can express them in terms of the expectation-value representation ⟨ ⟨ [ B ^ ^ † † ] J B ^ ^ K ⟩ ⟩ . In this case, the connection from ⟨ ⟨ [ B ^ ^ † † ] J B ^ ^ K ⟩ ⟩ to the density matrix is unique but can result in a numerically diverging series. This problem can be solved by introducing a cluster-expansion transformation (CET) that represents the distribution in terms of a Gaussian, defined by the singlet–doublet contributions, multiplied by a polynomial, defined by the higher-order clusters. It turns out that this formulation provides extreme convergence in representation-to-representation transformations.