arXiv subjects

Lijun Chen

Publications and source records attributed to Lijun Chen.

At least 55 records · Page 3Linked to original sources

arXiv2020

Quantum Experiments and Hypergraphs: Multi-Photon Sources for Quantum Interference, Quantum Computation and Quantum Entanglement

We introduce the concept of hypergraphs to describe quantum optical experiments with probabilistic multi-photon sources. Every hyperedge represents a correlated photon source, and every vertex stands for an optical output path. Such general graph description provides new insights for producing complex high-dimensional multi-photon quantum entangled states, which go beyond limitations imposed by pair creation via spontaneous parametric down-conversion. Furthermore, properties of hypergraphs can be investigated experimentally. For example, the NP-Complete problem of deciding whether a hypergraph has a perfect matchin can be answered by experimentally detecting multi-photon events in quantum experiments. By introducing complex weights in hypergraphs, we show a general many-particle quantum interference and manipulating entanglement in a pictorial way. Our work paves the path for the development of multi-photon high-dimensional state generation and might inspire new applications of quantum computations using hypergraph mappings.

quant-ph↗

arXiv2020

Phenomenology of complex structured light in turbulent air

The study of light propagation has been a cornerstone of progress in physics and technology. Recently, advances in control and shaping of light have created significant interest in the propagation of complex structures of light -- particularly under realistic terrestrial conditions. While theoretical understanding of this research question has significantly grown over the last two decades, outdoor-experiments with complex light structures are rare, and comparisons with theory have been nearly lacking. Such situations show a significant gap between theoretical models of atmospheric light behaviour and current experimental effort. Here, in an attempt to reduce this gap, we describe an interesting result of atmospheric models which are feasible for empirical observation. We analyze in detail light propagation in different spatial bases and present results of the theory that the influence of atmospheric turbulence is basis-dependent. Concretely, light propagating as eigenstate in one complete basis is stronger influenced by atmosphere than light propagating in a different, complete basis. We obtain these results by exploiting a family of the continuously adjustable, complete basis of spatial modes -- the Ince-Gauss modes. Our concrete numerical results will hopefully inspire experimental efforts and bring the theoretical and empirical study of complex light patterns in realistic scenarios closer together.

physics.optics↗

arXiv2020

100Mbps Reconciliation for Quantum Key Distribution Using a Single Graphics Processing Unit

An efficient error reconciliation scheme is important for post-processing of quantum key distribution (QKD). Recently, a multi-matrix low-density parity-check codes based reconciliation algorithm which can provide remarkable perspectives for high efficiency information reconciliation was proposed. This paper concerns the improvement of reconciliation performance. Multi-matrix algorithm is implemented and optimized on the graphics processing unit (GPU) to obtain high reconciliation throughput. Experimental results indicate that GPU-based algorithm can highly improve reconciliation throughput to an average 85.67 Mbps and a maximum 102.084 Mbps with typical code rate and efficiency. This is the best performance of reconciliation on GPU platform to our knowledge.

quant-ph↗

arXiv2020

Multi-matrix rate-compatible reconciliation for quantum key distribution

Key reconciliation of quantum key distribution (QKD) is the process of correcting errors caused by channel noise and eavesdropper to identify the keys of two legitimate users. Reconciliation efficiency is the most important figure for judging the quality of a reconciliation scheme. To improve reconciliation efficiency, rate-compatible technologies was proposed for key reconciliation, which is denoted as the single-matrix ratecompatible reconciliation (SRCR). In this paper, a recently suggested technique called multi-matrix reconciliation is introduced into SRCR, which is referred to as the multi-matrix rate-compatible reconciliation (MRCR), to further improve reconciliation efficiency and promote the throughput of SRCR. Simulation results show that MRCR we proposed outperforms SRCR in reconciliation efficiency and throughput.

quant-ph↗

arXiv2019

Utilizing Players' Playtime Records for Churn Prediction: Mining Playtime Regularity

In the free online game industry, churn prediction is an important research topic. Reducing the churn rate of a game significantly helps with the success of the game. Churn prediction helps a game operator identify possible churning players and keep them engaged in the game via appropriate operational strategies, marketing strategies, and/or incentives. Playtime related features are some of the widely used universal features for most churn prediction models. In this paper, we consider developing new universal features for churn predictions for long-term players based on players' playtime.

cs.HC↗

arXiv2019

Incentivized Exploration for Multi-Armed Bandits under Reward Drift

We study incentivized exploration for the multi-armed bandit (MAB) problem where the players receive compensation for exploring arms other than the greedy choice and may provide biased feedback on reward. We seek to understand the impact of this drifted reward feedback by analyzing the performance of three instantiations of the incentivized MAB algorithm: UCB, $\varepsilon$-Greedy, and Thompson Sampling. Our results show that they all achieve $\mathcal{O}(\log T)$ regret and compensation under the drifted reward, and are therefore effective in incentivizing exploration. Numerical examples are provided to complement the theoretical analysis.

cs.LG↗

arXiv2019

Accelerated Voltage Regulation in Multi-Phase Distribution Networks Based on Hierarchical Distributed Algorithm

We propose a hierarchical distributed algorithm to solve optimal power flow (OPF) problems that aim at dispatching controllable distributed energy resources (DERs) for voltage regulation at minimum cost. The proposed algorithm features unprecedented scalability to large multi-phase distribution networks by jointly exploring the tree/subtrees structure of a large radial distribution network and the structure of the linearized distribution power flow (LinDistFlow) model to derive a hierarchical, distributed implementation of the primal-dual gradient algorithm that solves OPF. The proposed implementation significantly reduces the computation loads compared to the centrally coordinated implementation of the same primal-dual algorithm without compromising optimality. Numerical results on a 4,521-node test feeder show that the designed algorithm achieves more than 10-fold acceleration in the speed of convergence compared to the centrally coordinated primal-dual algorithm through reducing and distributing computational loads.

math.OC↗

arXiv2019

Online Stochastic Optimization of Networked Distributed Energy Resources

This paper investigates distributed control and incentive mechanisms to coordinate distributed energy resources (DERs) with both continuous and discrete decision variables as well as device dynamics in distribution grids. We formulate a multi-period social welfare maximization problem, and based on its convex relaxation propose a distributed stochastic dual gradient algorithm for managing DERs. We further extend it to an online realtime setting with time-varying operating conditions, asynchronous updates by devices, and feedback being leveraged to account for nonlinear power flows as well as reduce communication overhead. The resulting algorithm provides a general online stochastic optimization algorithm for coordinating networked DERs with discrete power setpoints and dynamics to meet operational and economic objectives and constraints. We characterize the convergence of the algorithm analytically and evaluate its performance numerically.

math.OC↗

arXiv2019

Signal-Anticipation in Local Voltage Control in Distribution Systems

We consider the signal-anticipating behavior in local Volt/Var control for distribution systems. Such a behavior makes interaction among the nodes a game. We characterize Nash equilibrium of the game as the optimum of a global optimization problem and establish its asymptotic global stability. We also show that the signal-anticipating voltage control has less restrictive convergence condition than the signal-taking control. We then introduce the notion of Price of Signal-Anticipation (PoSA) to characterize the impact of signal-anticipating control, and use the gap in cost between network equilibrium in the signal-taking control and Nash equilibrium in the signal-anticipating control as the metric for PoSA. We characterize how the PoSA scales with the size, topology, and heterogeneity of the distribution network for a few network settings. Our results show that the PoSA is upper bounded by a constant and the average PoSA per node will go to zero as the size of the network increases. This is desirable as it means that the PoSA will not be arbitrarily large, no matter what the size of the network is, and no mechanism is needed to mitigate the signal-anticipating behavior. We further carry out numerical experiments with a real-world distribution circuit to complement the theoretical analysis.

math.OC↗

arXiv2019

Self-Organizing Quantum Networks

As the inevitable development trend of quantum key distribution, quantum networks have attracted extensive attention, and many prototypes have been deployed over recent years. Existing quantum networks based on optical fibers or quantum satellites can realize the metro and even global communications. However, for some application scenarios that require emergency or temporary communications, such networks cannot meet the requirements of rapid deployment, low cost, and high mobility. To solve this problem, we introduce an important concept of classical networks, i.e., self-organization, to quantum networks, and give two simple network prototypes based on acquisition, tracking, and pointing systems. In these networks, the users only need to deploy the network nodes, which will rapidly, automatically, and adaptively organize and mange a quantum network. Our method expands the application scope of quantum networks, and gives a new approach for the design and implementation of quantum networks. It also provides users with a low-cost access network solution, and can be used to fundamentally solve the security problem of classical self-organizing networks.

quant-ph↗

arXiv2019

Quantum Experiments and Graphs III: High-Dimensional and Multi-Particle Entanglement

Quantum entanglement plays an important role in quantum information processes, such as quantum computation and quantum communication. Experiments in laboratories are unquestionably crucial to increase our understanding of quantum systems and inspire new insights into future applications. However, there are no general recipes for the creation of arbitrary quantum states with many particles entangled in high dimensions. Here, we exploit a recent connection between quantum experiments and graph theory and answer this question for a plethora of classes of entangled states. We find experimental setups for Greenberger-Horne-Zeilinger states, W states, general Dicke states, and asymmetrically high-dimensional multipartite entangled states. This result sheds light on the producibility of arbitrary quantum states using photonic technology with probabilistic pair sources and allows us to understand the underlying technological and fundamental properties of entanglement.

quant-ph↗

arXiv2019

Hierarchical Distributed Voltage Regulation in Networked Autonomous Grids

We propose a novel algorithm to solve optimal power flow (OPF) that aims at dispatching controllable distributed energy resources (DERs) for voltage regulation at minimum cost. The proposed algorithm features unprecedented scalability to large distribution networks by utilizing an information structure based on networked autonomous grids (AGs). Specifically, each AG is a subtree of a large distribution network that has a tree topology. The topology and line parameters of each AG are known only to a regional coordinator (RC) that is responsible for communicating with and dispatching the DERs within this AG. The reduced network, where each AG is treated as a node, is managed by a central coordinator (CC), which knows the topology and line parameters of the reduced network only and communicates with all the RCs. We jointly explore this information structure and the structure of the linearized distribution power flow (LinDistFlow) model to derive a hierarchical, distributed implementation of the primal-dual gradient algorithm that solves the OPF. The proposed implementation significantly reduces the computation burden compared to the centrally coordinated implementation of the primal-dual algorithm. Numerical results on a 4,521-node test feeder show that the proposed hierarchical distributed algorithm can achieve an improvement of more than tenfold in the speed of convergence compared to the centrally coordinated primal-dual algorithm.

math.OC↗

arXiv2019

Multi-Matrix Post-Processing for Quantum Key Distribution

Post-processing is a significant step in quantum key distribution(QKD), which is used for correcting the quantum-channel noise errors and distilling identical corrected keys between two distant legitimate parties. Efficient error reconciliation protocol, which can lead to an increase in the secure key generation rate, is one of the main performance indicators of QKD setups. In this paper, we propose a multi-low-density parity-check codes based reconciliation scheme, which can provide remarkable perspectives for highly efficient information reconciliation. With testing our approach through data simulation, we show that the proposed scheme combining multi-syndrome-based error rate estimation allows a more accurate estimation about the error rate as compared with random sampling and single-syndrome estimation techniques before the error correction, as well as a significant increase in the efficiency of the procedure without compromising security and sacrificing reconciliation efficiency.

quant-ph↗

arXiv2018

Reverse and Forward Engineering of Local Voltage Control in Distribution Networks

The increasing penetration of renewable and distributed energy resources in distribution networks calls for real-time and distributed voltage control. In this paper we investigate local Volt/VAR control with a general class of control functions, and show that the power system dynamics with non-incremental local voltage control can be seen as distributed algorithm for solving a well-defined optimization problem (reverse engineering). The reverse engineering further reveals a fundamental limitation of the non-incremental voltage control: the convergence condition is restrictive and prevents better voltage regulation at equilibrium. This motivates us to design two incremental local voltage control schemes based on the subgradient and pseudo-gradient algorithms respectively for solving the same optimization problem (forward engineering). The new control schemes decouple the dynamical property from the equilibrium property, and have much less restrictive convergence conditions. This work presents another step towards developing a new foundation -- network dynamics as optimization algorithms -- for distributed realtime control and optimization of future power networks.

math.OC↗

arXiv2018

Demand Shaping in Cellular Networks

Demand shaping is a promising way to mitigate the wireless cellular capacity shortfall in the presence of ever-increasing wireless data demand. In this paper, we formulate demand shaping as an optimization problem that minimizes the variation in aggregate traffic. We design a distributed and randomized offline demand shaping algorithm under complete traffic information and prove its almost surely convergence. We further consider a more realistic setting where the traffic information is incomplete but the future traffic can be predicted to a certain degree of accuracy. We design an online demand shaping algorithm that updates the schedules of deferrable applications (DAs) each time when new information is available, based on solving at each timeslot an optimization problem over a shrinking horizon from the current time to the end of the day. We compare the performance of the online algorithm against the optimal offline algorithm, and provide numerical examples to complement the theoretical analysis.

math.OC↗

arXiv2017

Decomposition of Nonlinear Dynamical Systems Using Koopman Gramians

In this paper we propose a new Koopman operator approach to the decomposition of nonlinear dynamical systems using Koopman Gramians. We introduce the notion of an input-Koopman operator, and show how input-Koopman operators can be used to cast a nonlinear system into the classical state-space form, and identify conditions under which input and state observable functions are well separated. We then extend an existing method of dynamic mode decomposition for learning Koopman operators from data known as deep dynamic mode decomposition to systems with controls or disturbances. We illustrate the accuracy of the method in learning an input-state separable Koopman operator for an example system, even when the underlying system exhibits mixed state-input terms. We next introduce a nonlinear decomposition algorithm, based on Koopman Gramians, that maximizes internal subsystem observability and disturbance rejection from unwanted noise from other subsystems. We derive a relaxation based on Koopman Gramians and multi-way partitioning for the resulting NP-hard decomposition problem. We lastly illustrate the proposed algorithm with the swing dynamics for an IEEE 39-bus system.

eess.SY↗

arXiv2017

Stochastic Dual Algorithm for Voltage Regulation in Distribution Networks with Discrete Loads

This paper considers power distribution networks with distributed energy resources and designs an incentive-based algorithm that allows the network operator and customers to pursue given operational and economic objectives while concurrently ensuring that voltages are within prescribed limits. Heterogeneous DERs with continuous and discrete control commands are considered. We address four major challenges: discrete decision variables, non-convexity due to a Stackelberg game structure, unavailability of private information from customers, and asynchronous operation. Starting from a non-convex setting, we develop a distributed stochastic dual algorithm that solves a relaxed problem, and prove that the proposed algorithm achieves the global optimal solution of the original problem on average. Feasible values for discrete decision variables are also recovered. Stability of the algorithm is analytically established and numerically corroborated.

math.OC↗

arXiv2017

An Incentive-Based Online Optimization Framework for Distribution Grids

This paper formulates a time-varying social-welfare maximization problem for distribution grids with distributed energy resources (DERs) and develops online distributed algorithms to identify (and track) its solutions. In the considered setting, network operator and DER-owners pursue given operational and economic objectives, while concurrently ensuring that voltages are within prescribed limits. The proposed algorithm affords an online implementation to enable tracking of the solutions in the presence of time-varying operational conditions and changing optimization objectives. It involves a strategy where the network operator collects voltage measurements throughout the feeder to build incentive signals for the DER-owners in real time; DERs then adjust the generated/consumed powers in order to avoid the violation of the voltage constraints while maximizing given objectives. The stability of the proposed schemes is analytically established and numerically corroborated.

math.OC↗