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We consider a communication scenario where classical information is encodedin an ensemble of quantum states that admit a power series expansion in a costparameter and with the vanishing cost converge to a single zero-cost state. Fora given measurement scheme, we derive an approximate expression for mutualinformation in the leading order of the cost parameter. The general results areapplied to selected problems in optical communication, where coherent states oflight are used as input symbols and the cost is quantified as the averagenumber of photons per symbol. We show that for an arbitrary individualmeasurement on phase shift keyed (PSK) symbols, the photon informationefficiency is upper bounded by 2 nats of information per photon in the low-costlimit, which coincides with the conventional homodyne detection bound. Thepresented low-cost approximation facilitates a systematic analysis offew-symbol measurements that exhibit superadditivity of accessible information.For the binary PSK alphabet of coherent states, we present designs for two- andthree-symbol measurement schemes based on linear optics, homodyning, and singlephoton detection that offer respectively 2.49% and 3.40% enhancement relativeto individual measurements. We also show how designs for scalable superadditivemeasurement schemes emerge from the introduced low-cost formalism.

Low-cost limit of classical communication with restricted quantum measurements