QUANTUM ESTIMATION FOR QUANTUM TECHNOLOGY

Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine the value of these quantities should resort to indirect measurements and thus corresponds to a parameter estimation problem whose solution, i.e. the determination of the most precise estimator, unavoidably involves an optimization procedure. We review local quantum estimation theory and present explicit formulas for the symmetric logarithmic derivative and the quantum Fisher information of relevant families of quantum states. Estimability of a parameter is defined in terms of…