Surpassing the wave-particle duality relation via feed-forward of phase information

Complementarity constitutes a central aspect of quantum theory. It manifests itself, for example, in a two-way interferometer, where the simultaneous observation of an interference pattern and the acquisition of which-way information are limited by an inequality known as the duality relation. Here, we investigate which-way information in a double-slit interferometer and show that it can be correlated to the phase of the quantum object at the detection screen, leading to a phase-dependent which-way knowledge. In specific cases, this knowledge can locally exceed the limit set by the duality relation. Based on this observation, we propose a feed-forward protocol that aims at maximizing the which-way information locally for each phase after the particle has been recorded on the screen. This allows us to surpass the duality relation limit even globally. We present analytical results as a proof of principle of our protocol as well as numerical outcomes quantifying the amount of maximally achievable which-way knowledge.