Ponente
Descripción
The cornerstone of modern quantum metrology is the quantum Cramér-Rao bound and the quantum Fisher information. Under generic conditions, this bound can be saturated by an optimal estimator and measurement, provided that many repeated measurements on the system are performed. However, in the presence of smaller data sets it typically largely underestimates the error that can actually be achieved. In this talk, we present a family of generalized bounds on the variance of unbiased estimators that are larger than the quantum Cramér-Rao bound when the sample is small and thereby provide a more realistic limit on the achievable precision of a finite-sample quantum measurement. In the large-data limit, the hierarchy of bounds collapses back onto the quantum Cramér-Rao bound.
