Optimal Gaussian measurements for phase estimation in single-mode Gaussian metrology

The central issue in quantum parameter estimation is to find out the optimal measurement setup that leads to the ultimate lower bound of an estimation error. We address here a question of whether a Gaussian measurement scheme can achieve the ultimate bound for phase estimation in single-mode Gaussian metrology that exploits single-mode Gaussian probe states in a Gaussian environment. We identify three types of optimal Gaussian measurement setups yielding the maximal Fisher information depending on displacement, squeezing, and thermalization of the probe state. We show that the homodyne measurement attains the ultimate bound for both displaced thermal probe states and squeezed vacuum probe states, whereas for the other single-mode Gaussian probe states, the optimized Gaussian measurement cannot be the optimal setup, although they are sometimes nearly optimal. We then demonstrate that the measurement on the basis of the product quadrature operators $$\hat X\hat P + \hat P\hat X$$X̂P̂+P̂X̂, i.e., a non-Gaussian measurement, is required to be fully optimal.Quantum metrology: Optimal Gaussian measurementsOptimal measurement schemes have been identified for certain Gaussian states used in quantum information processing. Gaussian states are useful resources in quantum optical technologies as they are relatively easy to control, and can be employed to analyse quantum information processes. Such Gaussian states can be characterized using so-called Gaussian measurement schemes but it’s usually not so clear what the optimal measurement setups are. An international team of researchers led by Changhyoup Lee from the Karlsruhe Institute of Technology now identify optimal measurement setups to obtain phase information for different types of single-mode Gaussian states. Such an approach could be extended to other parameters, such as frequency, as well as to multi-mode Gaussian states, where entanglement starts to play an important role.