Abstract
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.
Highlights
In contrast to Bell inequalities which probe correlations between multiple spatially-separated systems [1,2,3], the Leggett-Garg inequalities (LGIs) test the temporal correlations of a single system [4,5,6]
The LGIs are based on two macrorealistic assumptions that intuitively hold in the world of our everyday experience: (i) macroscopic realism per se — that a system exists at all times in a macroscopically-distinct state; and (ii) non-invasive measurability — that it is possible to measure a system without disturbing it
Since both these assumptions fails under quantum mechanics, quantum systems can violate the LGIs
Summary
In contrast to Bell inequalities which probe correlations between multiple spatially-separated systems [1,2,3], the Leggett-Garg inequalities (LGIs) test the temporal correlations of a single system [4,5,6]. We report on LG experiments with single photons that implement a three-level quantum system measured with three orthogonal projectors We investigate both K3 and K4 inequalities and our main result is the observation of maximum values of the LG correlators K3 = 1.97 ± 0.06 and K4 = 2.96 ± 0.05, which clearly represent significant enhancements over the TTB. In contrast to our results for the LGI, where the measured violations are still lower than the theoretical maximum, our maximum measured value for the quantum witness saturates the theoretical bound for a three-outcome test [35], and presents a significant enhancement over the hitherto-observed value for a two-outcome case [29]. Our interferometeric set-up makes the designation of our measurements as INM extremely clear-cut
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