  The determination of entanglement measures in SU(N) gauge theories is a
non-trivial task. With the so-called "replica trick", a family of entanglement
measures, known as "R\'enyi entropies", can be determined with lattice Monte
Carlo. Unfortunately, the standard implementation of the replica method for
SU(N) lattice gauge theories suffers from a severe signal-to-noise ratio
problem, rendering high-precision studies of R\'enyi entropies prohibitively
expensive. In this work, we propose a method to overcome the signal-to-noise
ratio problem and show some first results for SU(N) in 4 dimensions.
