KTH/Nordita/SU seminar in Theoretical Physics

Reconstruction of quantum states as an inverse problem

by Göran Lindblad (KTH)

FA31 ()


Given the outcomes of a generalized measurement performed on an ensemble of N independent and identically prepared quantum systems, how do we best estimate the quantum state? We want to use the data as efficiently as possible, but as with other "inverse problems" such estimates are nonlinear in the data and can easily amplify the N-ensemble fluctuations to create spurious features in the solution, called "overfitting". I will sketch an iterative algorithm based on convex optimization and show some results of computer simulations. The simulations suggest a rule for terminating the iteration for a pretty good estimation of the state without overfitting (in the real world where we do not know the state). They also indicate that the accuracy is as good as we can expect for for a given measurement and a given N.