Quantum Detection and Estimation Theory

Carl W. Helstrom

Horace P. Yuen

Giacomo Mauro D’Ariano

Carl W. Helstrom

Statistical estimation theory applied to quantum mechanics and signal detection with optical instruments

Stewart D. Personick

Recent inquiries into optical communication have raised questions as to the validity of classical detection and estimation theory for weak light fields. Helstrom [1] proposed that the axioms of quantum mechanics be incorporated into a quantum approach to optical estimation and detection. In this paper, we discuss two important results, the quantum equivalent of the minimum-mean-square-error (MMSE) estimator and the quantum Cramér-Rao bound for estimation of the parameters of an electromagnetic field. The first result, a new one, is applied to linear modulation. We show that homodyning is the optimal demodulation scheme in that case. Parallels to the classical MMSE estimator are drawn. The Cramér-Rao bound, first derived in the quantum ease by Helstrom [1], is applied to specific estimation problems. Details are left to the references, but interesting results are presented.

Wenbin Yu, Baoyu Zheng, Shengmei Zhao

Coherent-states, representing electromagnetic radiation produced by physical devices such as lasers, are an important class of states for optical communications. For the coherent-state signal detection, a detection method basing on the POVM detection and the least-square estimation is proposed in this paper, concerning the quantum detection theory. This method has been proved to be effective in our paper, and the numerical results indicate that with this method we can fairly improve the performance of coherent-state signal detection.