  We consider a communication scenario where classical information is encoded
in an ensemble of quantum states that admit a power series expansion in a cost
parameter and with the vanishing cost converge to a single zero-cost state. For
a given measurement scheme, we derive an approximate expression for mutual
information in the leading order of the cost parameter. The general results are
applied to selected problems in optical communication, where coherent states of
light are used as input symbols and the cost is quantified as the average
number of photons per symbol. We show that for an arbitrary individual
measurement on phase shift keyed (PSK) symbols, the photon information
efficiency is upper bounded by 2 nats of information per photon in the low-cost
limit, which coincides with the conventional homodyne detection bound. The
presented low-cost approximation facilitates a systematic analysis of
few-symbol measurements that exhibit superadditivity of accessible information.
For the binary PSK alphabet of coherent states, we present designs for two- and
three-symbol measurement schemes based on linear optics, homodyning, and single
photon detection that offer respectively 2.49% and 3.40% enhancement relative
to individual measurements. We also show how designs for scalable superadditive
measurement schemes emerge from the introduced low-cost formalism.
