Measuring Trρ^n on Single Copies of ρ Using Random Measurements

Abstract

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

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