  Frequency correlations are a versatile and powerful tool which can be
exploited to perform spectral analysis of objects whose direct measurement
might be unfeasible. This is achieved through a so-called ghost spectrometer,
that can be implemented with quantum and classical resources alike. While there
are some known advantages associated to either choice, an analysis of their
metrological capabilities has not yet been performed. Here we report on the
metrological comparison between a quantum and a classical ghost spectrometer.
We perform the estimation of the transmittivity of a bandpass filter using
frequency-entangled photon pairs. Our results show that a quantum advantage is
achievable, depending on the values of the transmittivity and on the number of
frequency modes analyzed.
