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The stellar hierarchy of quantum states of light classifies the statesaccording to the Fock-state resources that are required for their generationtogether with unitary Gaussian operations. States with stellar rank n can bealso equivalently referred to as genuinely n-photon quantum non-Gaussianstates. Here we present an efficient method for construction of generalwitnesses of the stellar rank. The number of parameters that need to beoptimized in order to determine the witness does not depend on the stellar rankand it scales quadratically with the number of modes. We illustrate theprocedure by constructing stellar rank witnesses based on pairs of Fock stateprobabilities and also based on pairs of fidelities with superpositions ofcoherent states.

Efficient construction of witnesses of stellar rank of nonclassical states of light