  Entangled quantum states, such as N00N states, are of major importance for
quantum technologies due to their quantum-enhanced performance. At the same
time, their quantum correlations are relatively vulnerable when they are
subjected to imperfections. Therefore, it is crucial to determine under which
circumstances their distinct quantum features can be exploited. In this paper,
we study the entanglement property of noisy N00N states. This class of states
is a generalization of N00N states including various attenuation effects, such
as mixing, constant or fluctuating losses, and dephasing. To verify their
entanglement, we pursue two strategies: detection-based entanglement witnesses
and entanglement quasiprobabilities. Both methods result from our solution of
so-called separability eigenvalue equations. In particular, the entanglement
quasiprobabilities allow for a full entanglement characterization. As examples
of our general treatment, the cases of N00N states subjected to Gaussian
dephasing and fluctuating atmospheric losses are explicitly studied. In any
correlated fluctuating loss channel, entanglement is found to survive for
non-zero transmissivity. In addition, an extension of our approach to
multipartite systems is given, and the relation to the quantum-optical
nonclassicality in phase-space is discussed.
