For two symmetric quantum-state qualification tasks, the minimum error probability with N copies decays as N^{-3/2} exp(-N xi) for disjoint regions and (N F)^{-1/2} for adjacent regions, where xi and F are the Chernoff divergence and Fisher information of the worst-case boundary states.
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Universal Scaling of the Minimum Error Probability in Qualification of Quantum States
For two symmetric quantum-state qualification tasks, the minimum error probability with N copies decays as N^{-3/2} exp(-N xi) for disjoint regions and (N F)^{-1/2} for adjacent regions, where xi and F are the Chernoff divergence and Fisher information of the worst-case boundary states.