PT Journal
AU Gessner, M
   Smerzi, A
TI Hierarchies of Frequentist Bounds for Quantum Metrology: From Cramer-Rao to Barankin
SO Physical Review Letters
JI Phys. Rev. Lett.
PY 2023
BP 260801
EP 6pp
VL 130
IS 26
DI 10.1103/PhysRevLett.130.260801
LA English
AB We derive lower bounds on the variance of estimators in quantum metrology by choosing test observables that define constraints on the unbiasedness of the estimator. The quantum bounds are obtained by analytical optimization over all possible quantum measurements and estimators that satisfy the given constraints. We obtain hierarchies of increasingly tight bounds that include the quantum Cramer-Rao bound at the lowest order. In the opposite limit, the quantum Barankin bound is the variance of the locally best unbiased estimator in quantum metrology. Our results reveal generalizations of the quantum Fisher information that are able to avoid regularity conditions and identify threshold behavior in quantum measurements with mixed states, caused by finite data.
ER