Optimal violation of the Leggett–Garg inequality for arbitrary spin and emergence of classicality through unsharp measurements

• Optimal violation of Leggett–Garg inequality for arbitrary spin system.
• Quantitative study of coarse-graining through unsharp measurement.
• Emergence of classicality for any value of spin.

In the context of temporal correlations of particles with arbitrary spin, we obtain optimal violation of the Leggett–Garg inequality (LGI), improving upon an earlier result (Kofler, 2007 [24]). Our proof is accomplished through a suitable adaptation of a measurement scheme, previously employed for studying spatial correlations. We next consider unsharp measurements as a method of coarse graining, and show that LGI can not be violated below a precise value of the sharpness parameter. We then apply Fine's theorem in the context of LGI and derive a sufficient condition for emergence of classicality.