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We show that the quantum bound for temporal correlations in a Leggett-Garg test, analogous to the Tsirelson bound for spatial correlations in a Bell test, strongly depends on the number of levels $N$ that can be accessed by the measurement apparatus via projective measurements.
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For the Clauser-Horne-Shimony-Holt (CHSH) inequality [ 5 ] the maximum value under local hidden variables is 2 2 , the Tsirelson bound is 2 2 2\sqrt{2} , and the algebraic bound is 4 4
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