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We report a proof of the quantum Sanov Theorem by elementary application of basic facts about representations of the symmetric group, together with a complete characterization of the optimal error exponent in a situation where the null hypothesis is given by an arbitrarily varying quantum source instead. Our approach differs from previous ones in two points: First, it supports a reasoning inspired by the method of types. Second, the measurement scheme we propose to distinguish the twodoi:10.1088/1751-8113/47/23/235303 fatcat:blj35ejxo5djlpghgqnpx4doly