  Quantum illumination (QI) promises unprecedented performances in target
detection but there are various problems surrounding its implementation. Where
target ranging is a concern, signal and idler recombination forms a crucial
barrier to the protocol's success. This could potentially be mitigated if
performing a measurement on the idler mode could still yield a quantum
advantage. In this paper we investigate the QI protocol for a generically
correlated Gaussian source and study the phase-conjugating (PC) receiver,
deriving the associated SNR in terms of the signal and idler energies, and
their cross-correlations, which may be readily adapted to incorporate added
noise due to Gaussian measurements. We confirm that a heterodyne measurement
performed on the idler mode leads to a performance which asymptotically
approaches that of a coherent state with homodyne detection. However, if the
signal mode is affected by heterodyne but the idler mode is maintained clean,
the performance asymptotically approaches that of the PC receiver without any
added noise.
