Leggett--Garg inequality violations with a large ensemble of qubits

TL;DR

This paper explores how large ensembles of qubits, with their internal complexity and noise, can violate the Leggett--Garg inequality, providing insights into macroscopic quantum behavior and measurement strategies.

Contribution

It analyzes the impact of internal degrees of freedom and noise on Leggett--Garg inequality violations in large qubit ensembles, highlighting optimal measurement schemes.

Findings

Certain measurement schemes are more effective under noise.

Large ensembles can exhibit macroscopic quantum effects.

Internal structure influences violation visibility.

Abstract

We investigate how discrete internal degrees of freedom in a quasi-macroscopic system affect the violation of the Leggett--Garg inequality, a test of macroscopic-realism based on temporal correlation functions. As a specific example, we focus on an ensemble of qubits subject to collective and individual noise. This generic model can describe a range of physical systems, including atoms in cavities, electron or nuclear spins in NV centers in diamond, erbium in Y$_2$SiO$_5$, bismuth impurities in silicon, or arrays of superconducting circuits, to indicate but a few. Such large ensembles are potentially more macroscopic than other systems that have been used so far for testing the Leggett--Garg inequality, and open a route toward probing the boundaries of quantum mechanics at macroscopic scales. We find that, because of the non-trivial internal structure of such an ensemble, the behavior of different measurement schemes, under the influence of noise, can be surprising. We discuss which measurement schemes are optimal for flux qubits and NV centers, and some of the technological constraints and difficulties for observing such violations with present-day experiments.