In this second lecture we will revisit the Hypothesis testing and parameter estimation scenarios discussed in the previous lecture, except we shall be invoking quantum theory. In the case of quantum Hypothesis testing I shall review Holevo’s optimality theorem which establishes the conditions for achieving the maximum probability of success in a hypothesis testing scenario involving quantum states and measurements. We shall also cast these conditions in terms of semi-definite programs and apply them to obtain the optimal measurement (aka the Helstrom measurement) for the case of binary hypothesis testing. We will then consider quantum parameter estimation, review the quantum version of the Cramér-Rao bound and the Quantum Fisher Information (QFI). These concepts will be applied to the simple case of interferometry where we will encounter the Standard and Heisenberg limits in estimation precision.
