k-designs achieve maximal multi-copy discriminability for pure states when N suffices, mixed states outperform beyond that, and quantum offers quadratic advantage over classical in Bayes capacity terms.
Dimension witnesses and quantum state discrimination
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Dimension witnesses allow one to test the dimension of an unknown physical system in a device-independent manner, that is, without placing assumptions about the functioning of the devices used in the experiment. Here we present simple and general dimension witnesses for quantum systems of arbitrary Hilbert space dimension. Our approach is deeply connected to the problem of quantum state discrimination, hence establishing a strong link between these two research topics. Finally, our dimension witnesses can distinguish between classical and quantum systems of the same dimension, making them potentially useful for quantum information processing.
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The most discriminable quantum states in the multicopy regime
k-designs achieve maximal multi-copy discriminability for pure states when N suffices, mixed states outperform beyond that, and quantum offers quadratic advantage over classical in Bayes capacity terms.