Quantum mechanics offers new possibilities to process and transmit information. In recent years, algorithms and cryptographic protocols exploiting the superposition principle and the existence of entangled states have been designed. They should allow us to realize communication and computational tasks that outperform any classical strategy. Here we show that quantum mechanics also provides fresh perspectives in the field of random networks. Already the simplest model of a classical random graph changes markedly when extended to the quantum case, where we obtain a distinct behaviour of the critical probabilities at which different subgraphs appear. In particular, in a network of N nodes, any quantum subgraph can be generated by local operations and classical communication if the entanglement between pairs of nodes scales as N−2. This result also opens up new vistas in the domain of quantum networks and their applications.
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We acknowledge support from the EU projects ‘AQUTE’ and ‘QAP’, the ERC grant ‘PERCENT’ and ‘QUAGATUA’, the DPG excellence cluster ‘Munich Center for Advanced Photonics’ and FOR 635, the Spanish MEC Consolider QOIT and FIS2007-60182 and FIS2008-00784 projects, la Generalitat de Catalunya and Caixa Manresa, the Alexander von Humboldt Foundation and the QCCC programme of the Elite Network of Bavaria.
The authors declare no competing financial interests.
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Perseguers, S., Lewenstein, M., Acín, A. et al. Quantum random networks. Nature Phys 6, 539–543 (2010). https://doi.org/10.1038/nphys1665
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