Stereographic Geometry of Coherence and Which-path Information

TL;DR

This paper reveals a deep connection between stereographic projection geometry and the duality-entanglement behavior of single photons, showing that geometric representations can reflect fundamental quantum properties.

Contribution

It demonstrates that stereographic projection naturally encodes the duality-entanglement relation of single photons, linking geometric and quantum descriptions.

Findings

Stereographic projection relates to quantum duality and entanglement.

The geometry is sensitive to particle, wave, and entanglement properties.

The duality-entanglement relation emerges from stereographic geometry.

Abstract

Recently, it was shown that quantum entanglement is an indispensable part of the duality behavior of light. Here, we report a surprisingly intimate connection between the stereographic projection and the duality--entanglement nature of a single photon. We show that, the duality--entanglement relation [Optica \textbf{5}, 942 (2018)], naturally emerges from the stereographic projection geometry. We demonstrate that this geometry is complementarity sensitive; in the sense that, it is sensitive to the particle nature, wave nature, and entanglement nature of a single photon.