Aspects of Complementarity and Uncertainty

TL;DR

This paper analyzes the Einstein recoiling slit experiment, showing how entanglement and uncertainty principles underpin quantum complementarity and which-way detection.

Contribution

It demonstrates that entanglement and sum-uncertainty relations are fundamental to understanding complementarity in the two-slit experiment.

Findings

Entanglement between particle and slit explains complementarity.

Derivation of Englert-Greenberger-Yasin duality from entanglement.

Uncertainty relations relate to the which-way detection process.

Abstract

The two-slit experiment with quantum particles provides many insights into the behaviour of quantum mechanics, including Bohr's complementarity principle. Here we analyze Einstein's recoiling slit version of the experiment and show how the inevitable entanglement between the particle and the recoiling slit as a which-way detector is responsible for complementarity. We derive the Englert-Greenberger-Yasin duality from this entanglement, which can also be thought of as a consequence of sum-uncertainty relations between certain complementary observables of the recoiling slit. Thus, entanglement is an integral part of the which-way detection process, and so is uncertainty, though in a completely different way from that envisaged by Bohr and Einstein.