Path selection for quantum repeater networks
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Path selection for quantum repeater networks Rodney Van Meter1 (), Takahiko Satoh2, Thaddeus D. Ladd3,4, William J. Munro5, Kae Nemoto4 1. Faculty of Environment and Information Studies, Keio University, Fujisawa 252-0882, Japan 2. The University of Tokyo, Japan 3. Stanford University, Palo Alto, CA 94305, USA 4. National Institute of Informatics, Tokyo, Japan 5. NTT Basic Research Labs, Atsugi, Japan
Received: 9 July 2012/Revised: 1 April 2013/Accepted: 11 September 2013 © Tsinghua University Press and Springer-Verlag Berlin Heidelberg 2013
Abstract 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. Keywords quantum communication, quantum repeater, Dijkstra, path selection
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Introduction
A routing algorithm chooses a path on a graph, and consists of two parts: a definition for the cost of a single link, and a function for calculating the cost of a path based on those link costs, allowing us to extend a single pointto-point channel to a richer network. Dijkstra’s Shortest Path First algorithm, for example, takes a simple scalar cost for each link and treats the sum of link costs as a cost for a candidate path [1]. The emerging field of quantum communication has, to date, experimentally demonstrated the basic principles of entangled quantum networking [2,3,4,5,6], and laid the theoretical foundations of creating long-distance, high-quality entanglement [7,8,9], but topologically has considered primarily channels and linear networks, leaving E-mail: [email protected]
us with an urgent need for a path selection mechanism as quantum networks develop. Quantum key distribution (QKD) is probably the most prominent use of quantum communication, and commercial products are available [10,11,12]. In QKD, quantum effects (and a large dose of classical statistics) are used to detect the presence of an eavesdropper on the channel. QKD generates streams of shared, secret, random
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