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.
Quantum t-designs: t-wise independence in the quantum world
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A t-design for quantum states is a finite set of quantum states with the property of simulating the Haar-measure on quantum states, w.r.t. any test that uses at most t copies of a state. We give efficient constructions for approximate quantum t-designs for arbitrary t. We then show that an approximate 4-design provides a derandomization of the state-distinction problem considered by Sen (quant-ph/0512085), which is relevant to solving certain instances of the hidden subgroup problem.
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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.