Complementarity via error-free measurement in a two-path interferometer

TL;DR

This paper investigates the wave-particle duality in a Mach-Zehnder interferometer, demonstrating a complementary relation between fringe visibility and which-path information, with conditions for optimal measurement accuracy.

Contribution

It introduces an error-free measurement approach to quantify wave-particle complementarity in an asymmetric interferometer, deriving a precise relation between visibility and which-path information.

Findings

Derived the relation V + Ipath ≤ 1 for the interferometer

Identified conditions for equality in the complementarity relation

Proposed an error-free measurement method for which-path info

Abstract

We study both the wave-like behavior and particle-like behavior in a general Mach-Zehnder interferometer with its asymmetric beam splitter. A error-free measurement in the detector is used to extract the which-path information. The fringe visibility V and the which-path information Ipath are derived: their complementary relation V + Ipath less than or equal to 1 are found, and the condition for the equality is also presented.