The duality principle in the presence of postselection

TL;DR

This paper demonstrates that postselection can create an apparent violation of the quantum duality principle by allowing simultaneous high predictability and visibility, highlighting the influence of fair-sampling in such tests.

Contribution

It experimentally shows how postselection can lead to apparent violations of the duality principle, emphasizing the role of fair-sampling loopholes in quantum measurements.

Findings

Postselection enables simultaneous high predictability and visibility.

Apparent violations of the duality principle can be controlled experimentally.

Fair-sampling plays a crucial role in tests of quantum duality.

Abstract

The duality principle, a cornerstone of quantum mechanics, limits the coexistence of wave and particle behaviours of quantum systems. This limitation takes a quantitative form when applied to the visibility $\mathcal V$ and predictability $\mathcal P$ within a two-alternative system, which are bound by the inequality $\mathcal V^2+ \mathcal P^2 \leq 1$. However, if such a system is coupled to its environment, it becomes possible to obtain conditional measures of visibility and predictability, i.e.~measures that are conditional on the state of the environment. We show that in this case, the predictability and visibility values can lead to an apparent violation of the duality principle. We experimentally realize this apparent violation in a controlled manner by enforcing a fair-sampling-like loophole via postselection. Given the ability to simultaneously obtain high predictability information and high visibility interference fringes for a wide range of coupling strengths and postselected states, this work highlights the role of fair-sampling in tests of the duality principle.