Leggett-Garg inequalities for the statistics of electron transport

TL;DR

This paper derives Leggett-Garg inequalities for electron transport statistics, demonstrating how quantum systems can violate classical assumptions about macroscopic realism in charge transfer processes.

Contribution

It introduces a novel set of inequalities for the moment generating function in electron transport and shows their violation by quantum systems.

Findings

Violations observed in normal and superconducting single-electron transistors

Inequalities serve as tests for macroscopic realism in charge transport

Quantum effects can be distinguished from classical models using these inequalities

Abstract

We derive a set of Leggett-Garg inequalities (temporal Bell's inequalities) for the moment generating function of charge transferred through a conductor. Violation of these inequalities demonstrates the absence of a macroscopic-real description of the transport process. We show how these inequalities can be violated by quantum-mechanical systems and consider transport through normal and superconducting single-electron transistors as examples.