Entanglement buffers are systems that maintain high-quality entanglement, ensuring it is readily available for consumption when needed. We study the performance of a two-node buffer, where each node has one long-lived quantum memory for entanglement storage and multiple short-lived memories for generation. Freshly generated entanglement may be used to purify stored entanglement, which degrades over time. Stored entanglement may be removed due to consumption or failed purification. We derive analytical expressions for the entanglement availability and the average fidelity upon consumption. Our solutions are computationally efficient and provide fundamental bounds to the performance of purification-based entanglement buffers. We also show that purification must be performed as frequently as possible to maximise the average fidelity of entanglement upon consumption, even if this often leads to the loss of high-quality entanglement due to purification failures. Moreover, we obtain heuristics for the design of good purification policies in practical systems.

Quantum networks are envisioned to enable reliable distribution and manipulation of quantum information across distances, forming the foundation of a future quantum internet. The fair and efficient allocation of communication resources in such networks has been addressed through the quantum network utility maximization (QNUM) framework, which optimizes network utility under the assumption of predetermined routes for competing user demands. In this work, we relax this assumption and aim to identify optimal routes that correspond to the maximum achievable network utility. Specifically, we formulate the single-path utility-based entanglement routing problem as a Mixed-Integer Convex Program (MICP). The formulation is exact when negativity is chosen as the entanglement measure for utility quantification or the network supports sufficiently high entanglement generation rates across demands. For other entanglement measures considered, the formulation approximates the problem with over 99.99 % accuracy on evaluated real-world examples. To improve computational tractability, we propose a randomized rounding-based heuristic and an upper bound via the relaxation of the MICP. Furthermore, based on min-congestion routing, we introduce an alternative randomized heuristic and upper bound. This heuristic is computationally faster, while both the heuristic and the upper bound often outperform their counterparts on considered real-world networks. Our work provides the framework for extending classical flow-based and quality of service-aware routing concepts to quantum networks.

Network utility maximization (NUM) addresses the problem of allocating resources fairly within a network and explores the ways to achieve optimal allocation in real-world networks. Although extensively studied in classical networks, NUM is an emerging area of research in the context of quantum networks. In this work, we consider the quantum network utility maximization (QNUM) problem in a static setting, where a user's utility takes into account the assigned quantum quality (fidelity) via a generic entanglement measure, as well as the corresponding rate of entanglement generation. Under certain assumptions, we demonstrate that the QNUM problem can be formulated as an optimization problem with the rate allocation vector as the only decision variable. Using a change-of-variable technique known in the field of geometric programming, we then establish sufficient conditions under which this formulation can be reduced to a convex problem: a class of optimization problems that can be solved efficiently and with certainty even in high dimensions. We further show that this technique preserves convexity, enabling us to formulate convex QNUM problems in networks where some routes have certain entanglement measures that do not readily admit convex formulation while others do. This allows us to compute the optimal resource allocation in networks where heterogeneous applications run over different routes.