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

TL;DR

This paper addresses complementarity in two-way interferometers by showing that WW knowledge can be enhanced beyond the standard duality bound through a phase-aware, feed-forward strategy. The authors derive a phase-dependent WW knowledge $\mathcal{K}_{\hat{W}}(\delta)$ and propose a protocol that, after measuring the QO’s phase $\delta$ at the screen, selects a WW detector observable $\hat{W}_{\delta}$ that maximizes WW information for that phase. They provide analytical results for a simplified feed-forward scheme and numerical results for a full optimization, demonstrating both local and global surpassing of the duality relation, with maximum excesses $\approx 1.016$ and $\approx 1.025$ respectively for $0<\mathcal{V}<1$. The work emphasizes that the surpassing is consistent with duality once the fixed-observable assumption is lifted, and highlights practical considerations and potential experimental realizations (e.g., in Mach-Zehnder configurations). The findings suggest new avenues for phase-conditioned information processing in quantum optics and quantum information tasks that exploit feed-forward control. $

Abstract

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.

Figures (1)

• Figure 1: (a) Young-type double slit interferometer consisting of two pathways $a$ and $b$, two which-way detectors (WWD) within each pathway and a screen with an interference pattern $P(\delta)$. (b) Setup for experimental verification of the which-way knowledge. (c) Comparison of a fixed basis choice and the presented feed-forward protocol in a quantum circuit diagram. (d,e) Phase-dependent knowledge $\mathcal{K}_{\ldots}(\delta)$ (canonical $\hat{E}$: solid; natural $\hat{N}$: dashed; feed-forward $FF$: dots) for two different visibilities (d) $\mathcal{V} = 0.5$ and (e) $\mathcal{V} = 0.9$. (f) Sum of the phase-averaged knowledge $\overline{\mathcal{K}_{\ldots}(\delta)}$ squared and visibility $\mathcal{V}$ squared for the canonical knowledge ($\hat{E}$, solid), the simplified version of the feed-forward protocol ($\hat{N}/\hat{E}$, dashed), and the non-simplified feed-forward protocol ($FF$, dotted).