Extreme Violations of Leggett-Garg Inequalities for a System Evolving under Superposition of Unitaries

The violation of Leggett-Garg inequality (LGI) indicates general temporal correlations in quantum systems that cannot be explained classically. Under unitary dynamics and projective measurements, the violation of LGI is restricted up to the temporal Tsirelson's bound (TTB). Here, we consider superposition of unitary time evolutions and find them to produce an enhancement in the violation of LGI beyond the TTB, growing monotonically with increasing superposition. We experimentally realize superposition of unitaries in NMR systems and demonstrate this enhanced violation. In the presence of noise, such superposition of unitaries remarkably extend the time of LGI violation, showcasing improved robustness against decoherence. This opens up possibilities of employing such nontrivial dynamical maps for robust quantum control, along with provoking research on characterizing correlations in general sequential measurement scenarios.