Multipath wave-particle duality with a path detector in a quantum superposition

TL;DR

This paper theoretically analyzes a multipath interference experiment with a quantum superposition of a path detector's presence, demonstrating that wave-particle duality and complementarity are preserved, contrary to some claims of violation.

Contribution

It introduces a rigorous analysis of multipath interference with a superposed path detector, reaffirming the validity of wave-particle duality relations in such quantum scenarios.

Findings

Wave-particle duality relation is upheld in multipath superposition experiments.

Complementarity remains valid when correctly evaluating path distinguishability.

Apparent violations are due to misinterpretation of path information.

Abstract

According to Bohr's principle of complementarity, a quanton can behave either as a wave or a particle, depending on the choice of the experimental setup. Some recent two-path interference experiments have devised methods where one can have a quantum superposition of the two choices, thus indicating that a quanton may be in a superposition of wave and particle nature. These experiments have been of interest from the point of view of Wheeler's delayed-choice experiment. However, it has also been claimed that this experiment can violate complementarity. Here we theoretically analyze a multipath interference experiment that has a which-path detector in a quantum superposition of being present and absent. We show that a tight multipath wave-particle duality relation is respected in all such situations, and complementarity holds well. The apparent violation of complementarity may be due to incorrect evaluation of path distinguishability in such scenarios.