Complementarity via Minimum Error Measurement in a Two-Path Interferometer
Junzhao Liu, Yanjun Liu, Jing Lu**
Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics and Synergetic Innovation Center of Quantum Effects and Applications, Hunan Normal University, Changsha 410081
Abstract：We study the fringe visibility and the which-path information (WPI) of a general Mach–Zehnder interferometer with an asymmetric beam splitter (BS). A minimum error measurement in the detector is used to extract the WPI. Both the fringe visibility $V$ and the WPI $I_{\rm path}$ are affected by the initial state of the photon and the second asymmetric BS. The condition in which the WPI takes the maximum is obtained. The complementarity relationship $V^{2}+I_{\rm path}^{2}\leq 1$ is found, and the conditions for equality are also presented.
2019, Vol. 36 
