Leggett-Garg Inequalities

TL;DR

The paper reviews the Leggett-Garg inequalities, which test quantum coherence over time in single systems, highlighting recent experimental violations and discussing foundational issues like non-invasive measurement and loopholes.

Contribution

It provides an introduction to Leggett-Garg inequalities, reviews recent experimental violations, and discusses theoretical proposals and foundational challenges.

Findings

Experimental violations observed in superconducting qubits, nuclear spins, photons

Discussion of non-invasive measurement and clumsiness loophole

Recent theoretical proposals for applications in quantum transport and biology

Abstract

In contrast to the spatial Bell's inequalities, which probe entanglement between spatially-separated systems, the Leggett-Garg inequalities test the correlations of a single system measured at different times. Violation of a genuine Leggett-Garg test implies either the absence of a realistic description of the system or the impossibility of measuring the system without disturbing it. Quantum mechanics violates the inequalities on both accounts and the original motivation for these inequalities was as a test for quantum coherence in macroscopic systems. The last few years has seen a number of experimental tests and violations of these inequalities in a variety of microscopic systems such as superconducting qubits, nuclear spins, and photons. In this article, we provide an introduction to the Leggett-Garg inequalities and review these latest experimental developments. We discuss important topics such as the significance of the non-invasive measurability assumption, the clumsiness loophole, and the role of weak measurements. Also covered are some recent theoretical proposals for the application of Leggett-Garg inequalities in quantum transport, quantum biology and nano-mechanical systems.