We investigate the quantum entanglement entropy for the four-dimensional Euclidean SU(3) gauge theory. We present the first non-perturbative calculation of the entropic |c|-function (|$C(l)$|) of SU(3) gauge theory in lattice Monte Carlo simulation using the replica method. For |0 l 0.7| fm, where |l| is the length of the subspace, the entropic |c|-function is almost constant, indicating conformally invariant dynamics. The value of the constant agrees with that perturbatively obtained from free gluons, with 20% discrepancy. When |l| is close to the |Λ _ QCD⁻¹ (~ Tc⁻¹ )| scale, the entropic |c|-function decreases smoothly, and it is consistent with zero within error bars at |l 0.9| fm.
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A 2016 study studied this question.