We consider a recently proposed entity authentication protocol, in which a physical unclonable key is interrogated by random coherent states of light, and the quadratures of the scattered light are analysed by means of a coarse-grained homodyne detection. We derive a sufficient condition for the protocol to be secure against an emulation attack, in which an adversary knows the challenge-response properties of the key, and moreover he can access the challenges during the verification. The security analysis relies on Holevo's bound and Fano's inequality, and suggests that the protocol is secure against the emulation attack for a broad range of physical parameters that are within reach of today's technology.