  Entanglement boosts performance limits in sensing and communication, and
surprisingly the advantage over classical protocols can be even larger in
presence of entanglement-breaking noise. However, to maximally fulfill such
advantages requires an optimal measurement design, a challenging task as
information is encoded in the feeble quantum correlation after entanglement is
destroyed by loss and noise. For this reason, the optimal measurement design is
still elusive for various entanglement-enhanced protocols long after their
debut. We propose a conversion module to capture and transform the quantum
correlation to coherent quadrature displacement, which enables the optimal
receiver design for a wide range of entanglement-enhanced protocols, including
quantum illumination, phase estimation, classical communication, and arbitrary
thermal-loss channel pattern classification. Via heterodyne and passive linear
optics, the conversion module maps the multi-mode quantum detection problem to
the semi-classical detection problem of a single-mode noisy coherent state, so
that explicit measurements can be constructed to achieve the optimal
performance. Our module provides a paradigm of processing noisy quantum
correlations for near-term implementation.
