A Nonlocal Wave-Particle Duality

TL;DR

This paper introduces a nonlocal duality relation in a modified ghost-interference experiment, linking the particle's path information to the entangled partner's interference, extending complementarity to a nonlocal context.

Contribution

It derives a new nonlocal duality relation and proposes a ghost quantum eraser, advancing understanding of nonlocal wave-particle duality in quantum mechanics.

Findings

Derived a nonlocal duality relation ${ m D}_1^2 + { m V}_2^2 \, \le \, 1$

Showed that measuring one particle's path hides the other's wave nature

Proposed a ghost quantum eraser to restore interference fringes

Abstract

We propose and analyze a modified ghost-interference experiment, and show that revealing the particle-nature of a particle passing through a double-slit hides the wave-nature of a spatially separated particle which it is entangled with. We derive a nonlocal duality relation, ${\mathcal D}_1^2 + {\mathcal V}_2^2 \le 1$, which connects the path distinguishability of one particle to the interference visibility of the other. It extends Bohr's principle of complementarity to a nonlocal scenario. We also propose a ghost quantum eraser in which, erasing the which-path information of one particle brings back the interference fringes of the other.