Information Theoretical Analysis of Quantum Metrology

We address the framework of analysing quantum metrology in the information-theoretic picture. Firstly we show how to extract the maximum amount of information in general via suitable state initialization of the probes at the beginning and a quantum measurement at the end. Our analysis can apply to both the single-parameter and the multi-parameter estimation procedures as well as to any other quantum information processing procedures. We then establish a direct connection between the information-theoretic picture of quantum metrology and its conventional variance-covariance picture, by showing that any estimation procedure achieves Heisenberg limit in variance-covariance picture can also reach the information-theoretic Heisenberg limit in the asymptotic sense. As a direct consequence, we argue that the entangled measurement is not necessary for achieving Heisenberg limit in the information-theoretic pictures, which is explicitly illustrated for the Quantum-Classical parallel strategy of quantum metrology with a separable measurement employed and the Heisenberg limit saturated in both pictures.