Abstract
The optimal allocation of resources is a crucial task for their efficient use in a wide range of practical applications in science and engineering. This paper investigates the optimal allocation of resources in multipartite quantum systems. In particular, we show the relevance of proportional fairness and optimal reliability criteria for the application of quantum resources. Moreover, we present optimal allocation solutions for an arbitrary number of qudits using measurement incompatibility as an exemplary resource theory. Besides, we study the criterion of optimal equitability and demonstrate its relevance to scenarios involving several resource theories such as nonlocality vs local contextuality. Finally, we highlight the potential impact of our results for quantum networks and other multi-party quantum information processing, in particular to the future Quantum Internet.
Highlights
In our daily lives, we perform various activities to meet our needs, fulfill our desires or achieve our goals
The solution to the above problem is the optimal allocation of resources and defines a well-established research area applied in various fields, including operations research, economics, computing, communication networks, and ecology [6, 7, 8, 9, 10, 11, 12, 13]
A variety of approaches are used to determine the practical value of quantum systems, such as cryptography, communication capacity, computational complexity and thermodynamics
Summary
We perform various activities to meet our needs, fulfill our desires or achieve our goals. These activities require the use of physical objects, which may be within our reach or require a provider. Online meetings provide a timely example, in which it is possible to understand intuitively the allocation criteria used in this work. We will use this example to present the criteria studied, but for brevity, we will postpone the formal definitions to section 4. We study the equitability criteria for resource theories with tradeoffs between them and show how this applies to quantum multi-resource scenarios
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