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

Changhun Oh, Changhyoup Lee, Carsten Rockstuhl, Hyunseok Jeong, Jaewan Kim, Hyunchul Nha, Su Yong Lee

Research output: Contribution to journalArticle

7 Citations (Scopus)


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 X̂ P̂ + P̂ X̂ , i.e., a non-Gaussian measurement, is required to be fully optimal.

Original languageEnglish
Article number10
Journalnpj Quantum Information
Issue number1
Publication statusPublished - 1 Dec 2019


ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Statistical and Nonlinear Physics
  • Computer Networks and Communications
  • Computational Theory and Mathematics

Cite this