# Temporal Bell inequality measured

Among the most puzzling aspects of quantum physics is the measurement process being most drastically posed by Schrödinger’s cat paradox. Schrödinger envisaged a (quantum) cat trapped inside a box equipped with some device which may, randomly, kill the cat. Quantum mechanics tells us that at any time, if unobserved, the cat is both dead and alive. However, if the system is probed, for instance by opening the box, we will find the cat in one of the two possible states, either alive or dead. According to the formalism of quantum mechanics, this result is nondeterministic; i.e. the outcome of our measurement – and therefore the (classical) state of the

cat – is not even defined before opening the box. But how can we know that quantum mechanics is not simply incomplete, and that there are not other ‘‘hidden’’ variables on which the state of the cat depends, thus rendering the measurement deterministic? When formulated in the context of spatially separated subsystems, this type of argument leads to the celebrated Bell’s inequality, which limits the strength of the statistical correlations between distant subsystems within a local realistic theory. On the other hand, in contexts where locality is not relevant, the focus is on the premises of realism and the characterization of the type of temporal (vs spatial) correlations that would emerge within this realist description.

This issue was first investigated by Leggett and Garg in 1985 and led to the formulation of the so-called temporal Bell inequalities (TBI). The major difference to the original Bell inequalities is that instead of correlations between states of two spatially separated systems, one is now concerned with correlations of the state of a single system at different points in time. A measurable inequality is obtained from the assumptions of macroscopic realism (a macroscopic system is always in one of its macroscopically distinct states) and thus the possibility to perform noninvasive measurements (measurements do not influence the dynamics of the system). It is clear that these assumptions, and therefore the resulting inequality, are typically violated by quantum mechanics. However, we would expect these assumptions to become valid at some point as the considered system becomes closer and closer to a truly macroscopic object. Within this view TBIs which have been measured in a recent publication in PRL [Waldherr et al. Phys. Rev. Lett 107, 129901 2011] provide a criterion to characterize the boundary between the quantum and classical domains and the possible identification of macroscopic quantum coherence.

Temporal Bell inequality as measured by a single nitrogen nuclear spin of a diamond defect. The curve shows the temporal correlations of measurements on a single spin as this spin is subject to forced coherent oscillations.