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While it is known that Tr(\rho^n) can be measured directly (i.e., withoutfirst reconstructing the density matrix) by performing joint measurements on ncopies of the same state rho, it is shown here that random measurements onsingle copies suffice, too. Averaging over the random measurements directlyyields estimates of Tr(\rho^n), even when it is not known what measurementswere actually performed (so that one cannot reconstruct \rho).

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