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

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