  We develop a quantum learning scheme for binary discrimination of coherent
states of light. This is a problem of technological relevance for the reading
of information stored in a digital memory. In our setting, a coherent light
source is used to illuminate a memory cell and retrieve its encoded bit by
determining the quantum state of the reflected signal. We consider a situation
where the amplitude of the states produced by the source is not fully known,
but instead this information is encoded in a large training set comprising many
copies of the same coherent state. We show that an optimal global measurement,
performed jointly over the signal and the training set, provides higher
successful identification rates than any learning strategy based on first
estimating the unknown amplitude by means of Gaussian measurements on the
training set, followed by an adaptive discrimination procedure on the signal.
By considering a simplified variant of the problem, we argue that this is the
case even for non-Gaussian estimation measurements. Our results show that, even
in absence of entanglement, collective quantum measurements yield an
enhancement in the readout of classical information, which is particularly
relevant in the operating regime of low-energy signals.
