Quantum Clock Synchronization with a Single Qudit

Clock synchronization for nonfaulty processes in multiprocess networks is indispensable for a variety of technologies. A reliable system must be able to resynchronize the nonfaulty processes upon some components failing causing the distribution of incorrect or conflicting information in the network. The task of synchronizing such networks is related to detectable Byzantine agreement (DBA), which can classically be solved using recursive algorithms if and only if less than one-third of the processes are faulty. Here we introduce a nonrecursive quantum algorithm that solves the DBA and achieves clock synchronization in the presence of arbitrary many faulty processes by using only a single quantum system

Randomized protocols for asynchronous consensus

The famous Fischer, Lynch, and Paterson impossibility proof shows that it is impossible to solve the consensus problem in a natural model of an asynchronous distributed system if even a single process can fail. Since its publication, two decades of work on fault-tolerant asynchronous consensus algorithms have evaded this impossibility result by using extended models that provide (a) randomization, (b) additional timing assumptions, (c) failure detectors, or (d) stronger synchronization mechanisms than are available in the basic model. Concentrating on the first of these approaches, we illustrate the history and structure of randomized asynchronous consensus protocols by giving detailed descriptions of several such protocols.Comment: 29 pages; survey paper written for PODC 20th anniversary issue of Distributed Computin

Fast Agreement in Networks with Byzantine Nodes

We study Consensus in synchronous networks with arbitrary connected topologies. Nodes may be faulty, in the sense of either Byzantine or proneness to crashing. Let t denote a known upper bound on the number of faulty nodes, and D_s denote a maximum diameter of a network obtained by removing up to s nodes, assuming the network is (s+1)-connected. We give an algorithm for Consensus running in time t + D_{2t} with nodes subject to Byzantine faults. We show that, for any algorithm solving Consensus for Byzantine nodes, there is a network G and an execution of the algorithm on this network that takes ?(t + D_{2t}) rounds. We give an algorithm solving Consensus in t + D_{t} communication rounds with Byzantine nodes using authenticated messages of polynomial size. We show that for any numbers t and d > 4, there exists a network G and an algorithm solving Consensus with Byzantine nodes using authenticated messages in fewer than t + 3 rounds on G, but all algorithms solving Consensus without message authentication require at least t + d rounds on G. This separates Consensus with Byzantine nodes from Consensus with Byzantine nodes using message authentication, with respect to asymptotic time performance in networks of arbitrary connected topologies, which is unlike complete networks. Let f denote the number of failures actually occurring in an execution and unknown to the nodes. We develop an algorithm solving Consensus against crash failures and running in time ?(f + D_{f}), assuming only that nodes know their names and can differentiate among ports; this algorithm is also communication-efficient, by using messages of size ?(mlog n), where n is the number of nodes and m is the number of edges. We give a lower bound t+D_t-2 on the running time of any deterministic solution to Consensus in (t+1)-connected networks, if t nodes may crash

Multi-party Quantum Byzantine Agreement Without Entanglement

In this paper we propose a protocol of quantum communication to achieve Byzantine agreement among multiple parties. The striking feature of our proposal in comparison to the existing protocols is that we do not use entanglement to achieve the agreement. There are two stages in our protocol. In the first stage, a list of numbers that satisfies some special properties is distributed to every participant by a group of semi-honest list distributors via quantum secure communication. Then, in the second stage those participants exchange some information to reach agreement.Comment: 6 pages, 1 figur

Path Selection for Quantum Repeater Networks

Quantum networks will support long-distance quantum key distribution (QKD) and distributed quantum computation, and are an active area of both experimental and theoretical research. Here, we present an analysis of topologically complex networks of quantum repeaters composed of heterogeneous links. Quantum networks have fundamental behavioral differences from classical networks; the delicacy of quantum states makes a practical path selection algorithm imperative, but classical notions of resource utilization are not directly applicable, rendering known path selection mechanisms inadequate. To adapt Dijkstra's algorithm for quantum repeater networks that generate entangled Bell pairs, we quantify the key differences and define a link cost metric, seconds per Bell pair of a particular fidelity, where a single Bell pair is the resource consumed to perform one quantum teleportation. Simulations that include both the physical interactions and the extensive classical messaging confirm that Dijkstra's algorithm works well in a quantum context. Simulating about three hundred heterogeneous paths, comparing our path cost and the total work along the path gives a coefficient of determination of 0.88 or better.Comment: 12 pages, 8 figure