The power of random measurements: measuring Tr(ρ^n) on single copies of ρ

Abstract

While it is known that Tr(ρ^n) can be measured directly (i.e., without first reconstructing the density matrix) by performing joint measurements on n copies of the same state rho, it is shown here that random measurements on single copies suffice, too. Averaging over the random measurements directly yields estimates of Tr(ρ^n), even when it is not known what measurements were actually performed (so that one cannot reconstruct ρ).

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