Exact evaluation of the stabilizer Rényi entropy of a Greenberger–Horne–Zeilinger state

The stabilizer Rényi entropy (SRE) is a key metric for nonstabilizerness, or quantum magic, that measures the extent to which a quantum state deviates from the stabilizer framework. In this paper we present a calculation of the vanishing SRE of a Greenberger–Horne–Zeilinger (GHZ) stabilizer state from its matrix product state representation. We focus here on a demonstrative and exact proof that applies for all chain lengths.