Information Theoretical Analysis of Quantum Metrology

We establish a direct connection between the recently proposed information theoretic picture of quantum metrology and its conventional root-mean-square-error (RMSE) picture. A complement is conceived of the information-theoretic quantum metrology by showing that any estimation procedure achieves Heisenberg limit in RMSE picture also have the information-theoretic Heisenberg limit for which entangled measurement is not necessary. We explicitly present a Quantum-Classical Parallel strategy of quantum metrology which employs a separable measurement and saturates the Heisenberg limit in both pictures.