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Frontiers in Optics

Recovery of distributed quantum information in quantum networks

Ankur Raina, Priya J. Nadkarni, Shayan Garani Srinivasa

Published Jan 1, 2017• 1 citation
Publisher

Abstract

We use quantum networks to store quantum information in a distributed setting. We propose recovery methods to restore the stored quantum information in the event of failure of any of the nodes of the network.
DOI
10.1364/fio.2017.jw4a.38

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Quantum graph states are highly entangled quantum states known to exhibit properties useful in applications such as quantum error correction, quantum computation, etc. We distribute quantum information across nodes, each having a qubit at its location, by using encoding techniques. We call it a quantum graph state code. By modeling the loss of a qubit due to failure of a node as a quantum erasure, we present a recovery mechanism for distributed quantum information using purification followed by an error correction procedure.
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Abstract We consider entanglement-based quantum networks where information is stored in a delocalized way within regions or the whole network. This offers a natural protection against failure of network nodes, loss and decoherence, and has built-in security features. Quantum information is transmitted within the network by performing local measurements on individual nodes only. Information can be localized within regions or at a specific node by collaborative actions using only entanglement within a region, or sometimes even without entanglement. We discuss several examples based on error correction stabilizer codes, Dicke states and correlation space encodings. We show how to design fully functional networks using encoded states or correlation space resources.
Distributed quantum information stored over nodes within a quantum network are prone to node failures, motivating the need for coded quantum networks. We encode kkk qubits of quantum information over an nnn-node network in a distributed fashion, with one qubit per node, using modified graph-state codes. We devise a procedure to recover the encoded quantum information in any given arbitrary network after a detected node fails. The recovery procedure is locally within four edges of the failed node. For a network with even number of nodes, we provide a class of scalable modified graph-state codes with rate $(n\ensuremath{-}2)/n$, saturating the quantum Singleton bound. This yields higher coding rates than Grassl et al.'s well-known erasure codes and has asymptotic rate 1. For odd node size nnn, we design the network links to obtain an $(n\ensuremath{-}3)/n$ rate-optimal modified graph state code.
Quantum networks use properties of quantum mechanics to transfer of data securely. Quantum entanglement is exploited in quantum networks to transfer information from one network node to another. Two nodes can transfer data using quantum teleportation when they share entangled pairs of qubits. Hence, efficient mechanism to distribute entanglement among quantum network nodes is a necessity. To the best of the knowledge of the authors, proposed entanglement distribution methods are primarily based on current state of network parameters, such as, fidelities, etc. None of them consider historical usage of entangled qubits in transferring data to set up entanglement between nodes. This paper presents a novel way to establish connection between two nodes using history of previous data transfers over quantum links and proactively distribute entanglement among intermediate nodes to speed up connection setup process. Results show, in a quantum network of 20 nodes, the proposed approach reduces connection failure rate from 25% for one connection to 5% for fifty connections.