  Spectroscopy is an important tool for probing the properties of materials,
chemicals and biological samples. We design a practical transmitter-receiver
system that exploits entanglement to achieve a provable quantum advantage over
all spectroscopic schemes based on classical sources. To probe the absorption
spectra, modelled as pattern of transmissivities among different frequency
modes, we employ broad-band signal-idler pairs in two-mode squeezed vacuum
states. At the receiver side, we apply photodetection after optical parametric
amplification. Finally, we perform a maximal-likehihood decision test on the
measurement results, achieving orders-of-magnitude-lower error probability than
the optimum classical systems in various examples, including `wine-tasting' and
`drug-testing' where real molecules are considered. In detecting the presence
of an absorption line, our quantum scheme achieves the optimum performance
allowed by quantum mechanics. The quantum advantage in our system is robust
against noise and loss, which makes near-term experimental demonstration
possible.
