  Distinguishing quantum states that admit a classical counterpart from those
that exhibit nonclassicality has long been a central issue in quantum optics.
Finding an implementable criterion certifying optical nonclassicality (i.e, the
incompatibility with a statistical mixture of coherent states) is of major
importance as it often is a prerequisite to quantum information processes. A
hierarchy of conditions for detecting whether a quantum state exhibits optical
nonclassicality can be written based on some matrices of moments of the optical
field [Phys. Rev. A 72, 043808 (2005)]. Here, we design optical nonclassicality
observables that act on several replicas of a quantum state and whose
expectation value coincides with the determinant of these matrices, hence
providing witnesses of optical nonclassicality that overcome the need for state
tomography. These multicopy observables are used to construct a family of
physically implementable schemes involving linear optical operations and photon
number detectors.
