Complementarity via Minimum Error Measurement in a Two-Path Interferometer*

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 Ipath 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 path 2 ≤ 1 is found, and the conditions for equality are also presented.

Fringe visibility and correlation in Mach–Zehnder interferometer with an asymmetric beam splitter

“…[11][12][13][14][15][16][17][18][19] In addition, the complementary relationship in a general MZI with an asymmetric beam splitter (BS) has also attracted great attention. [20][21][22][23][24][25][26][27][28][29] Originally, the uncertainty principle was attributed to the absence of interference fringe. Ever since the proposal that the entanglement is responsible for the loss of interference, [30] a detector is introduced to the MZI, which is capable of making the path taken by the interfering particle and called the whichpath detector (WPD).…”