Duality relation and joint measurement in a Mach-Zehnder Interferometer

Understand

The Mach-Zehnder interferometric setup quantitatively characterizing the wave-particle duality implements in fact a joint measurement of two unsharp observables.

• We present a necessary and sufficient condition for such a pair of unsharp observables to be jointly measurable.
• The condition is shown to be equivalent to a duality inequality, which for the optimal strategy of extracting the which-path information is more stringent than the Jaeger-Shimony-Vaidman-Englert inequality.