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Leggett-Garg inequalities are tests of macroscopic realism that can be violated by quantum mechanics. In this letter, we realise photonic Leggett-Garg tests on a three-level system and implement measurements that admit three distinct measurement outcomes, rather than the usual two. In this way we obtain violations of three- and four-time Leggett-Garg inequalities that are significantly in excess of those obtainable in standard Leggett-Garg tests. We also report violations the quantum-witness equality up to the maximum permitted for a three-outcome measurement. Our results highlight differences between spatial and temporal correlations in quantum mechanics.

Uncertainty relations are the hallmarks of quantum physics and have been widely investigated since its original formulation. To understand and quantitatively capture the essence of preparation uncertainty in quantum interference, the uncertainty relations for unitary operators need to be investigated. Here, we report the first experimental investigation of the uncertainty relations for general unitary operators. In particular, we experimentally demonstrate the uncertainty relation for general unitary operators proved by Bagchi and Pati [ Phys. Rev. A94, 042104 (2016)], which places a non-trivial lower bound on the sum of uncertainties and removes the triviality problem faced by the product of the uncertainties. The experimental findings agree with the predictions of quantum theory and respect the new uncertainty relation.