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Very roughly speaking, yes, "entangled measures" (that is, global measures on multiple copies) make it easier to distinguish states. The intuitive reason is that, if $\langle\rho,\sigma\rangle\equiv\operatorname{Tr}(\rho\sigma)<1$, then $\langle\rho^{\otimes n},\sigma^{\otimes n}\rangle=\langle\rho,\sigma\rangle^n$, which decreases with ...


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