# Fringe visibility and distinguishability in two-path interferometer with an asymmetric beam splitter

## TL;DR

This paper analyzes how asymmetry in a Mach-Zehnder interferometer's beam splitter affects fringe visibility and distinguishability, deriving bounds and conditions for optimal quantum interference.

## Contribution

It provides a general analysis of fringe visibility and distinguishability in asymmetric interferometers, including bounds and conditions for pure and mixed input states.

## Key findings

- Maximum fringe visibility occurs when Sx=0 and beta=pi/2.
- The complementary relation V^2 + D^2 <= 1 is established.
- Conditions for equality in the complementarity are identified.

## Abstract

We study the fringe visibility and the distinguishability of a general Mach-Zehnder interferometer with an asymmetric beam splitter. Both the fringe visibility V and the distinguishability D are affected by the input state of the particle characterized by the Bloch vector S=(Sx,Sy,Sz) and the second asymmetric beam splitter characterized by paramter /beta. For the total system is initially in a pure state, it is found that the fringe visibility reaches the upper bound and the distinguishability reaches the lower bound when cos(/beta) = -Sx. The fringe visibility obtain the maximum only if Sx = 0 and /beta = /pi/2 when the input particle is initially in a mixed state. The complementary relationship V2 + D2 <= 1 is proved in a general Mach-Zehnder interferometer with an asymmetric beam splitter, and the conditions for the equality are also presented.

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Source: https://tomesphere.com/paper/1812.04348