  Quantum features of correlated optical modes define a major aspect of the
nonclassicality in quantized radiation fields. However, the phase-sensitive
detection of a two-mode light field is restricted to interferometric setups and
local intensity measurements. Even the full reconstruction of the quantum state
of a single radiation mode relies on such detection layouts and the preparation
of a well-defined reference light field. In this work, we establish the notion
of the essential quantum correlations of two-mode light fields. It refers to
those quantum correlations which are measurable by a given device, i.e., the
accessible part of a nonclassical Glauber-Sudarshan phase-space distribution,
which does not depend on a global phase. Assuming a simple four-port
interferometer and photon-number-resolving detectors, we derive the
reconstruction method and nonclassicality criteria based on the
Laplace-transformed moment-generating function of the essential
quasiprobability. With this technique, we demonstrate that the essential
quantum correlations of a polarization tomography scheme are observable even if
the detectors are imperfect and cannot truly resolve the photon statistics.
