On the Fidelity Distribution of Link-level Entanglements under Purification

Quantum entanglement is the key to quantum communications over considerable distances. The first step for entanglement distribution among quantum communication nodes is to generate link-level Einstein-Podolsky-Rosen (EPR) pairs between adjacent communication nodes. EPR pairs may be continuously generated and stored in a few quantum memories to be ready for utilization by quantum applications. A major challenge is that qubits suffer from unavoidable noise due to their interaction with the environment, which is called decoherence. This decoherence results in the known exponential decay model of the fidelity of the qubits with time, thus, limiting the lifetime of a qubit in a quantum memory and the performance of quantum applications. In this paper, we evaluate the fidelity of the stored EPR pairs under two opposite dynamical and probabilistic phenomena, first, the aforementioned decoherence and second purification, i.e. an operation to improve the fidelity of an EPR pair at the expense of sacrificing another EPR pair. Instead of applying the purification as soon as two EPR pairs are generated, we introduce a Purification scheme Beyond the Generation time (PBG) of two EPR pairs. We analytically show the probability distribution of the fidelity of stored link-level EPR pairs in a system with two quantum memories at each node allowing a maximum of two stored EPR pairs. In addition, we apply a PBG scheme that purifies the two stored EPR pairs upon the generation of an additional one. We finally provide numerical evaluations of the analytical approach and show the fidelity-rate trade-off of the considered purification scheme

A Comprehensive Analysis of Swarming-based Live Streaming to Leverage Client Heterogeneity

Due to missing IP multicast support on an Internet scale, over-the-top media streams are delivered with the help of overlays as used by content delivery networks and their peer-to-peer (P2P) extensions. In this context, mesh/pull-based swarming plays an important role either as pure streaming approach or in combination with tree/push mechanisms. However, the impact of realistic client populations with heterogeneous resources is not yet fully understood. In this technical report, we contribute to closing this gap by mathematically analysing the most basic scheduling mechanisms latest deadline first (LDF) and earliest deadline first (EDF) in a continuous time Markov chain framework and combining them into a simple, yet powerful, mixed strategy to leverage inherent differences in client resources. The main contributions are twofold: (1) a mathematical framework for swarming on random graphs is proposed with a focus on LDF and EDF strategies in heterogeneous scenarios; (2) a mixed strategy, named SchedMix, is proposed that leverages peer heterogeneity. The proposed strategy, SchedMix is shown to outperform the other two strategies using different abstractions: a mean-field theoretic analysis of buffer probabilities, simulations of a stochastic model on random graphs, and a full-stack implementation of a P2P streaming system.Comment: Technical report and supplementary material to http://ieeexplore.ieee.org/document/7497234

Collaborative Uploading in Heterogeneous Networks: Optimal and Adaptive Strategies

Collaborative uploading describes a type of crowdsourcing scenario in networked environments where a device utilizes multiple paths over neighboring devices to upload content to a centralized processing entity such as a cloud service. Intermediate devices may aggregate and preprocess this data stream. Such scenarios arise in the composition and aggregation of information, e.g., from smartphones or sensors. We use a queuing theoretic description of the collaborative uploading scenario, capturing the ability to split data into chunks that are then transmitted over multiple paths, and finally merged at the destination. We analyze replication and allocation strategies that control the mapping of data to paths and provide closed-form expressions that pinpoint the optimal strategy given a description of the paths' service distributions. Finally, we provide an online path-aware adaptation of the allocation strategy that uses statistical inference to sequentially minimize the expected waiting time for the uploaded data. Numerical results show the effectiveness of the adaptive approach compared to the proportional allocation and a variant of the join-the-shortest-queue allocation, especially for bursty path conditions.Comment: 15 pages, 11 figures, extended version of a conference paper accepted for publication in the Proceedings of the IEEE International Conference on Computer Communications (INFOCOM), 201

Inverse Reinforcement Learning in Swarm Systems

Inverse reinforcement learning (IRL) has become a useful tool for learning behavioral models from demonstration data. However, IRL remains mostly unexplored for multi-agent systems. In this paper, we show how the principle of IRL can be extended to homogeneous large-scale problems, inspired by the collective swarming behavior of natural systems. In particular, we make the following contributions to the field: 1) We introduce the swarMDP framework, a sub-class of decentralized partially observable Markov decision processes endowed with a swarm characterization. 2) Exploiting the inherent homogeneity of this framework, we reduce the resulting multi-agent IRL problem to a single-agent one by proving that the agent-specific value functions in this model coincide. 3) To solve the corresponding control problem, we propose a novel heterogeneous learning scheme that is particularly tailored to the swarm setting. Results on two example systems demonstrate that our framework is able to produce meaningful local reward models from which we can replicate the observed global system dynamics.Comment: 9 pages, 8 figures; ### Version 2 ### version accepted at AAMAS 201

Motif-based mean-field approximation of interacting particles on clustered networks

Interacting particles on graphs are routinely used to study magnetic behavior in physics, disease spread in epidemiology, and opinion dynamics in social sciences. The literature on mean-field approximations of such systems for large graphs typically remains limited to specific dynamics, or assumes cluster-free graphs for which standard approximations based on degrees and pairs are often reasonably accurate. Here, we propose a motif-based mean-field approximation that considers higher-order subgraph structures in large clustered graphs. Numerically, our equations agree with stochastic simulations where existing methods fail

Hypergraphon mean field games

We propose an approach to modeling large-scale multi-agent dynamical systems allowing interactions among more than just pairs of agents using the theory of mean field games and the notion of hypergraphons, which are obtained as limits of large hypergraphs. To the best of our knowledge, ours is the first work on mean field games on hypergraphs. Together with an extension to a multi-layer setup, we obtain limiting descriptions for large systems of non-linear, weakly interacting dynamical agents. On the theoretical side, we prove the well-foundedness of the resulting hypergraphon mean field game, showing both existence and approximate Nash properties. On the applied side, we extend numerical and learning algorithms to compute the hypergraphon mean field equilibria. To verify our approach empirically, we consider a social rumor spreading model, where we give agents intrinsic motivation to spread rumors to unaware agents, and an epidemic control problem.Recent developments in the field of complex systems have shown that real-world multi-agent systems are often not restricted to pairwise interactions, bringing to light the need for tractable models allowing higher-order interactions. At the same time, the complexity of analysis of large-scale multi-agent systems on graphs remains an issue even without considering higher-order interactions. An increasingly popular and tractable approach of analysis is the theory of mean field games. We combine mean field games with higher-order structure by means of hypergraphons, a limiting description of very large hypergraphs. To motivate our model, we build a theoretical foundation for the limiting system, showing that the limiting system has a solution and that it approximates finite, sufficiently large systems well. This allows us to analyze otherwise intractable, large hypergraph games with theoretical guarantees, which we verify using two examples of rumor spreading and epidemics control