  We derive tight quadratic inequalities for all kinds of hybrid
separable-inseparable $n$-particle density operators on an arbitrary
dimensional space. This methodology enables us to truly derive a tight
quadratic inequality as tests for full $n$-partite entanglement in various
Bell-type correlation experiments on the systems that may not be identified as
a collection of qubits, e.g., those involving photons measured by incomplete
detectors. It is also proved that when the two measured observables are assumed
to precisely anti-commute, a stronger quadratic inequality can be used as a
witness of full $n$-partite entanglement.
