Characterizing the information capacity of volume holograms with the Holevo bound

We show that Holevo's inequality upper-bounds the information capacity of a volume hologram without requiring a specification of the implementation of the hologram or the measurements to be made on the field scattered by the hologram. We find that, in the weakly scattering limit, the information capacity is not determined by the number of possible configurations of the holographic medium but only by the specification of the incident fields in the medium volume, which are determined at the volume boundary. By treating a volume hologram as a quantum communication channel, we establish a correspondence between the reconstruction of a hologram with multiple incident and scattered waves and the measurement of a quantum state with an operator-valued measure. We determine a bound on the probability of communications error, which describes the degree to which the incident fields may be distinguished by measurements of the scattered waves or, in other words, the crosstalk between the incident fields.