# Quantum wave-particle superposition in a delayed-choice experiment

## TL;DR

This paper demonstrates a quantum delayed-choice experiment with photons, controlling wave and particle states and phase, to directly observe quantum wave-particle superposition and test the complementarity principle beyond previous methods.

## Contribution

It introduces a novel quantum delayed-choice setup with remote state control, enabling direct observation of wave-particle superposition and fundamental tests of quantum complementarity.

## Key findings

- Successfully controlled wave and particle states of photons.
- Realized wave-particle transitions in classical and quantum scenarios.
- Performed tests of the complementarity principle beyond earlier experiments.

## Abstract

Wave-particle duality epitomizes the counterintuitive character of quantum physics. A striking illustration is the quantum delay-choice experiment, which is based on Wheeler's classic delayed-choice gedanken experiment, but with the addition of a quantum-controlled device enabling wave-to-particle transitions. Here we realize a quantum delayed-choice experiment in which we control the wave and the particle states of photons and in particular the phase between them, thus directly establishing the created quantum nature of the wave-particle. We generate three-photon entangled states and inject one photon into a Mach--Zehnder interferometer embedded in a 187-m-long two-photon Hong-Ou-Mandel interferometer. The third photon is sent 141m away from the interferometers and remotely prepares a two-photon quantum gate according to independent active choices under Einstein locality conditions. We have realized transitions between wave and particle states in both classical and quantum scenarios, and therefore tests of the complementarity principle that go fundamentally beyond earlier implementations.