  Understanding quantum phenomena which go beyond classical concepts is a focus
of modern quantum physics. Here, we show how the theory of nonnegative
polynomials emerging around Hilbert's 17th problem, can be used to optimally
exploit data capturing the nonclassical nature of light. Specifically, we show
that nonnegative polynomials can reveal nonclassicality in data even when it is
hidden from standard detection methods up to now. Moreover, the abstract
language of nonnegative polynomials also leads to a unified mathematical
approach to nonclassicality for light and spin systems, allowing us to map
methods for one to the other. Conversely, the physical problems arising also
inspire several mathematical insights into characterisation of nonnegative
polynomials.
