Measuring Trρn on single copies of ρ using random measurements

Phys Rev Lett. 2012 Mar 16;108(11):110503. doi: 10.1103/PhysRevLett.108.110503. Epub 2012 Mar 16.


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).