For energy-bounded bosonic states, a pure state is non-Gaussian exactly when its complex-extended position wavefunction has at least one zero, and the number of zeros equals the stellar rank.
Combinatorial Models of Creation-Annihilation
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Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial structures and the reduction to normal form of operator polynomials in such an algebra. The connection is achieved through suitable labelled graphs, or "diagrams", that are composed of elementary "gates". In this way, many normal form evaluations can be systematically obtained, thanks to models that involve set partitions, permutations, increasing trees, as well as weighted lattice paths. Extensions to q-analogues, multivariate frameworks, and urn models are also briefly discussed.
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On the complex zeros of the wavefunction
For energy-bounded bosonic states, a pure state is non-Gaussian exactly when its complex-extended position wavefunction has at least one zero, and the number of zeros equals the stellar rank.