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Experimental violation of the Leggett-Garg inequality with a single-spin system

Investigation the boundary between quantum mechanical description and classical realistic view is of fundamental importance. The Leggett-Garg inequality provides a criterion to distinguish between quantum systems and classical systems, and can be used to prove the macroscopic superposition state. A larger upper bound of the LG function can be obtained in a multi-level system. Here, we present an experimental violation of the Leggett-Garg inequality in a three-level system using nitrogen-vacancy center in diamond by ideal negative result measurement. The experimental maximum value of Leggett-Garg function is $K_{3}^{exp}=1.625\pm0.022$ which exceeds the Lüders bound with a $5σ$ level of confidence.