Abstract
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 Xhat P + hat Phat X, i.e., a non-Gaussian measurement, is required to be fully optimal.
Highlights
Gaussian states are useful resources in quantum optical technology.[1,2,3,4] Their intrinsic features that enable full analytical calculations for any Gaussian states and operations have attracted intensive interests from the theoretical perspective in many scientific areas
We look for an optimal Gaussian measurement setup for the phase estimation with single-mode Gaussian probe states
For single-mode Gaussian probe states classified to three types, we explore whether the optimal Gaussian measurement schemes can constitute the optimal measurement setup
Summary
Gaussian states are useful resources in quantum optical technology.[1,2,3,4] Their intrinsic features that enable full analytical calculations for any Gaussian states and operations have attracted intensive interests from the theoretical perspective in many scientific areas. Their experimental control is less demanding compared to those required for non-Gaussian states such as Fock states. They offer much promising building blocks for quantum information processing from a practical point of view.
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