  Quantum hypothesis testing is one of the most fundamental problems in quantum
information theory, with crucial implications in areas like quantum sensing,
where it has been used to prove quantum advantage in a series of binary
photonic protocols, e.g., for target detection or memory cell readout. In this
work, we generalize this theoretical model to the multi-partite setting of
barcode decoding and pattern recognition. We start by defining a digital image
as an array or grid of pixels, each pixel corresponding to an ensemble of
quantum channels. Specializing each pixel to a black and white alphabet, we
naturally define an optical model of barcode. In this scenario, we show that
the use of quantum entangled sources, combined with suitable measurements and
data processing, greatly outperforms classical coherent-state strategies for
the tasks of barcode data decoding and classification of black and white
patterns. Moreover, introducing relevant bounds, we show that the problem of
pattern recognition is significantly simpler than barcode decoding, as long as
the minimum Hamming distance between images from different classes is large
enough. Finally, we theoretically demonstrate the advantage of using quantum
sensors for pattern recognition with the nearest neighbor classifier, a
supervised learning algorithm, and numerically verify this prediction for
handwritten digit classification.
