Measuring Trρn on Single Copies of ρ Using Random Measurements

While it is known that Tr rho(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 rho(n), even when it is not known what measurements were actually performed (\so that rho cannot be reconstructed).