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The Internet, networks of connections between Hollywood actors, etc., are examples of complex networks, whose properties have been intensively studied in recent times. The 'small-world' property (that everyone has a few-step connection to celebrities), for instance, is a famous example.

A group of scientists led by Prof. J.I. Cirac, Director at the Max Planck Institute of Quantum Optics (Garching near Munich) and Leader of the Theory Division, has now introduced complex networks in the quantum realm. In a study appearing in the journal Nature Physics, the scientists show that these quantum complex networks have surprising properties: even in a very weakly connected quantum network, performing some measurements and other simple quantum operations allows the generation of arbitrary graphs of connections that are otherwise impossible in their classical counterparts.

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Quantum random networks

S. Perseguers1, M. Lewenstein2,3, A. Acín2,3 & J. I. Cirac1

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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