  This work analyzes the quantum corrections to holographic entanglement
entropy at first subleading order in $G_{N}$ due to photon excited states in
AdS. We compute the vacuum-subtracted von Neumann entropy of a $U(1)$ current
excited state for a polar cap region on the cylinder in any large-$N$,
strongly-coupled CFT$_{d}$ holographically dual to weakly-coupled Einstein
gravity for any dimension $d>2$. We then quantize a Maxwell field in
AdS$_{d+1}$ dual to the $U(1)$ current and consider a photon excited state
whose vacuum-subtracted generalized entropy for the entanglement wedge is
calculated. In order to factorise the Maxwell Hilbert space in AdS, we
construct an extended Hilbert space and the corresponding electromagnetic edge
modes. We find exact agreement between the CFT entanglement entropy and AdS
generalized entropy without the inclusion of entropy of the edge modes.
Finally, we show via explicit calculation that the contribution to the
vacuum-subtracted von Neumann entropy from electromagnetic edge modes indeed
vanishes, which is crucial for consistency with known holographic entropy
formulas.
