Conditions for Quantum Violation of Macrorealism in Large-spin Limit

Abstract

This study investigates the emergence of macroscopic classical behavior from quantum foundations via the entropic Leggett--Garg inequality. We introduce a geometric framework for deriving entropic Leggett--Garg inequalities with higher-order temporal correlations and demonstrate their advantages over conventional formulations. Numerical analyses show that entropic Leggett--Garg inequalities offer a robust and complementary criterion to standard approaches, providing a transparent information theoretic interpretation that facilitates the characterization of coherent quantum processes. By applying the WKB approximation, we prove that violations for maximally mixed states remain bounded by a constant in the macroscopic limit, indicating that macrorealism dominates in generic parameter regimes. We further explain previously reported maximal violations at specific parameter regimes as a consequence of the breakdown of the WKB approximation. Our findings indicate that quantum and classical descriptions remain macroscopically incompatible, while violations persist only in fine-tuned regimes, clarifying the conditions for detecting macroscopic quantum phenomena.