Reconstruction of quantum states as an inverse problem
by
Göran Lindblad(KTH)
→
Europe/Stockholm
FA31
FA31
Description
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.
