Ghost imaging as loss estimation: Quantum versus classical schemes

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.