The Leggett-Garg inequality in electron interferometers

TL;DR

This paper explores how electronic Mach-Zehnder interferometers can demonstrate violations of the Leggett-Garg inequality using non-invasive, time-resolved measurements, with implementations in quantum Hall edge channels and double quantum dots.

Contribution

It introduces a novel approach to test quantum coherence in electronic systems without invasive measurements, leveraging interferometer geometry for Leggett-Garg inequality violations.

Findings

Leggett-Garg inequality can be violated in electron interferometers

Correlation functions can be obtained without time-resolved measurements

Ideal negative measurements enable non-invasive testing

Abstract

We consider the violation of the Leggett-Garg inequality in electronic Mach-Zehnder inteferometers. This set-up has two distinct advantages over earlier quantum-transport proposals: firstly, the required correlation functions can be obtained without time-resolved measurements. Secondly, the geometry of an interferometer allows one to construct the correlation functions from ideal negative measurements, which addresses the non-invasiveness requirement of the Leggett-Garg inequality. We discuss two concrete realisations of these ideas: the first in quantum Hall edge-channels, the second in a double quantum dot interferometer.