Abstract
The Mach–Zehnder interferometer is a particularly simple device for demonstrating the wave-particle duality. This duality is particularly exhibited in the quantum delayed choice experiment where one realizes a superposition of wave- and particle-like behaviors. Considering this experiment as a generalized measurement described by a positive operator–valued measure (POVM), it realizes a joint measurement of path and interference obeying some duality relations.
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Notes
Martens inequality: Consider two generalized observables represented by two POVMs {Mm} and {Nn} which are non-ideal measurements of two PVMs {Pm} and {Qn}:
\( {M}_m=\sum \limits_{m^{\prime }}{\lambda}_{m{m}^{\prime }}{P}_{m^{\prime }} \), \( {\lambda}_{m{m}^{\prime }}\ge 0 \), \( \sum \limits_{m^{\prime }}{\lambda}_{m{m}^{\prime }}=1 \),
\( {N}_n=\sum \limits_{n^{\prime }}{\mu}_{n{n}^{\prime }}{Q}_{n^{\prime }} \), \( {\mu}_{n{n}^{\prime }}\ge 0 \), \( \sum \limits_{n^{\prime }}{\mu}_{n{n}^{\prime }}=1 \).
If {Mm} and {Nn} are jointly measurable, then \( {J}_{\left(\lambda \right)}+{J}_{\left(\mu \right)}\ge -\ln \left\{\underset{m,n}{\max } Tr\left({P}_m{Q}_n\right)\right\} \) (see [17]).
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Bendahane, M., El Atiki, M. & Kassou-Ou-Ali, A. The Quantum Delayed Choice Experiment Revisited. Braz J Phys 50, 52–56 (2020). https://doi.org/10.1007/s13538-019-00722-0
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DOI: https://doi.org/10.1007/s13538-019-00722-0