Quantum mechanical violation of macrorealism for large spin and its robustness against coarse-grained measurements

摘要

For multilevel spin systems, robustness of the quantum mechanical (QM)violation of macrorealism (MR) with respect to coarse grained measurements isinvestigated using three different necessary conditions of MR, namely, theLeggett-Garg inequality (LGI), Wigner's form of the Leggett-Garg inequality(WLGI) and the condition of no-signalling in time (NSIT). It is shown that fordichotomic sharp measurements, in the asymptotic limit of spin, the algebraicmaxima of the QM violations of all these three necessary conditions of MR areattained. Importantly, the QM violations of all these persist in that limiteven for \textit{arbitrary} unsharp measurements, i.e. for any non zero valueof the sharpness parameter characterizing the degree of fuzziness of therelevant measurements. We also find that when different measurement outcomesare clubbed into two groups for the sake of dichotomising the outcomes, theasymmetry/symmetry in the number of outcomes in the two groups, signifying thedegree of coarse graining of measurements, has a crucial role in discerningquantum violation of MR. The results clearly demonstrate that classicality doesnot emerges in the asymptotic limit of spin, whatever be the unsharpness anddegree of coarse graining of the measurements.