Delocalized information in quantum networks

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. the approach we follow here the failure of one (or several) individual nodes may have only a very limited influence, thereby minimizing the influence of network node failures. (ii) With respect to security of the stored information, the accessible information per node is bounded and can be made arbitrarily small. This implies that multiple nodes need to cooperate in order to access the information, while it is protected against malicious parties. In this context it is also interesting to note that the entanglement shared between an individual party and the rest of the network can be small [33], significantly less than one ebit. (iii) Since information is no longer stored in its bare form, one has to think of encoding, decoding and processing of information. Ideally, this should be done by local operations on individual nodes only, however it may also require some (restricted) amount of shared entanglement. In fact we find that processing of information, in particular transport among an entanglement-based network, is always possible using local operations only [34,35].We consider two different scenarios: (a) storage networks, where quantum information is stored in a distributed way among all or multiple nodes, and (b) generic networks with full functionality, including transport, that are comprised of different connected regions. Each region consists of multiple network nodes and corresponds to a single logical qubit. Regarding (a), we analyze several kind of encodings, where the logical basis states are given by codewords of error correction stabilizer codes, Dicke states [36][37][38], or resource states that have been discussed in the context of quantum computation in correlation space [33][34][35]. The usage of error correction codes for storage is well known and has been widely discussed. Such an approach offers protection against noise or loss, however requires active error correction. When used in a distributed scenario as we consider here, entanglement or non-local operations are required to detect and correct errors. Dicke state encodings in contrast have passive, built in protection features. Even without active error correction, quantum information is only slightly disturbed by loss, decoherence and node failures of a restricted amount of parties. Furtherm...

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