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.

中文翻译：

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具有受限量子测量的经典通信的低成本限制

我们考虑一个通信场景，其中经典信息被编码在一个量子态的集合中，该集合允许成本参数中的幂级数展开，并且消失的成本收敛到单个零成本状态。对于给定的测量方案，我们以成本参数的前导顺序推导出互信息的近似表达式。一般结果应用于光通信中的选定问题，其中光的相干状态用作输入符号，成本量化为每个符号的平均光子数。我们表明，对于相移键控 (PSK) 符号的任意单个测量，光子信息效率的上限为低成本限制中每个光子 2 nat 的信息，这与传统的零差检测界限一致。所提出的低成本近似有助于对少数符号测量进行系统分析，这些测量表现出可访问信息的超可加性。对于相干态的二进制 PSK 字母表，我们提出了基于线性光学、零差和单光子检测的双符号和三符号测量方案的设计，相对于单个测量分别提供 2.49% 和 3.40% 的增强。我们还展示了可扩展的超可加性测量方案的设计是如何从引入的低成本形式主义中产生的。和单光子检测相对于单个测量分别提供 2.49% 和 3.40% 的增强。我们还展示了可扩展的超可加性测量方案的设计是如何从引入的低成本形式主义中产生的。和单光子检测相对于单个测量分别提供 2.49% 和 3.40% 的增强。我们还展示了可扩展的超可加性测量方案的设计是如何从引入的低成本形式主义中产生的。