Quantum Twist to Complementarity: A Duality Relation

TL;DR

This paper derives a duality relation in quantum experiments with superposed which-way detectors, showing that each particle behaves either as a wave or a particle, thus preserving Bohr's complementarity.

Contribution

It introduces a new inequality bounding interference visibility and which-way information in modified quantum experiments with superposed detectors.

Findings

Single detections contribute to either wave or particle subensemble

The inequality constrains simultaneous wave and particle information

Bohr's complementarity remains valid in these experiments

Abstract

Some recent works have introduced a quantum twist to the concept of complementarity, exemplified by a setup in which the which-way detector is in a superposition of being present and absent. It has been argued that such experiments allow measurement of particle-like and wave-like behavior at the same time. Here we derive an inequality which puts a bound on the visibility of interference and the amount of which-way information that one can obtain, in the context of such modified experiments. As the wave-aspect can only be revealed by an ensemble of detections, we argue that in such experiments, a single detection can contribute only to one subensemble, corresponding to either wave-aspect or particle aspect. This way, each detected particle behaves either as particle or as wave, never both, and Bohr's complementarity is fully respected.