[GS_C_BSM] Alternative form of quantum Fisher information and extended quantum Cramer-Rao inequality
ABSTRACT
An alternative form of quantum Fisher information (QFI) that directly uses the inverse of the density operator defined within its positive Hilbert subspace is employed to extend the quantum Cramer-Rao inequality (QCRI) for general physical observables. A clear and general proof is provided for the fact that the alternative QFI serves as the upper bound for the conventional QFI based on logarithmic derivative or the inverse of symmetrization super-operator. An extended QCRI allows simple derivation of a quantum speed limit with tighter numerical factor, produces a temperature-energy uncertainty relation valid even for strong coupling regime, and results in a general inequality for the ratio of a quantum fluctuation of arbitrary physical observable to its time derivative. This new inequality has significant implications for practical applications of quantum thermodynamics and quantum sensing.
