A numerical framework makes it possible to certify the nonclassicality of bosonic systems from measured occupation probabilities, without the need to reconstruct the full state. The method builds optimal linear nonclassicality witnesses by solving a semi-infinite linear program, and recovers known analytical criteria as special cases, substantially enlarging the region of nonclassical states that can be detected.

Certifying nonclassicality — properties such as photon bunching or negativity of the Wigner function — usually requires full quantum tomography, a process costly in resources and measurement time. Criteria based directly on the occupation statistics of the bosonic mode bypass that step, but until now only a limited set of analytical inequalities existed. The new work completes that library by allowing optimal witnesses to be generated from arbitrary subsets of measured occupation probabilities.

As a case study, the authors apply the method to the resonant Jaynes-Cummings model with thermal states. The analysis reveals nonclassicality at short interaction times and close to thermal balance, two regimes where detecting nonclassicality is especially difficult with existing criteria. The team releases an open-source implementation of the numerical optimization together with the analytical criteria, so that the framework can be applied directly to occupation statistics measured across diverse bosonic platforms, from cold atoms to quantum optics.