Network Utility Maximization (NUM) is a mathematical framework that has endowed researchers with powerful methods for designing and analyzing classical communication protocols. NUM has also enabled the development of distributed algorithms for solving the resource allocation problem, while at the same time providing certain guarantees, e.g., that of fair treatment, to the users of a network. We extend here the notion of NUM to quantum networks, and propose three quantum utility functions -- each incorporating a different entanglement measure. We aim both to gain an understanding of some of the ways in which quantum users may perceive utility, as well as to explore structured and theoretically-motivated methods of simultaneously servicing multiple users in distributed quantum systems. Using our quantum NUM constructions, we develop an optimization framework for networks that use the single-photon scheme for entanglement generation, which enables us to solve the resource allocation problem while exploring rate-fidelity tradeoffs within the network topologies that we consider. We learn that two of our utility functions, which are based on distillable entanglement and secret key fraction, are in close agreement with each other and produce similar solutions to the optimization problems we study. Our third utility, based on entanglement negativity, has more favorable mathematical properties, and tends to place a higher value on the rate at which users receive entangled resources, compared to the two previous utilities, which put a higher emphasis on end-to-end fidelity. These contrasting behaviors thus provide ideas regarding the suitability of quantum network utility definitions to different quantum applications.
翻译:网络最小化是一个数学框架,使研究人员拥有设计和分析经典通信协议的强大方法。 NUM还帮助开发了用于解决资源分配问题的分布式算法,同时向网络用户提供某些保障,例如公平待遇的保障。我们在这里将NUM的概念扩大到量子网络,并提议三个量子效用功能 -- -- 每种功能都包含不同的纠缠度。我们的目标是了解量子用户可能看到效用的某些方法,并探索在分布式量子定义系统中同时为多个用户服务的结构性和理论上驱动的方法。我们利用量子 NUM的构建,为使用单发式组合生成的网络提供某些保障,例如公平待遇。我们在这里将NUM的概念扩大到量子网络的理念,并提议三个量子公用事业功能 -- -- 每一个都包含不同的纠缠和秘密关键分数,我们的目标都是要了解两种基于可蒸馏性粘结的量度和秘密关键分数的效用功能,它们彼此接近,同时为分布式质量定义的多个用户同时服务结构。我们用量子计算出一个最高级的解决方案,也就是我们研究的数学比例,我们研究前两个端值的数值,我们研究的用途,我们研究的数值比重的数值,也就是两个用途,我们更接近于前值的数值,我们研究的数值,我们研究的数值的数值, 的基点点点点的。