There is more and more concern about quantum communication and quantum network, I have some questions that I keep thinking for a while:(adsbygoogle = window.adsbygoogle || []).push({});

Could there be combination of the Network theory and Quantum theory?

Babarasi put forward the former one about 10 years ago and got great success.

Believing that it will absolutely be helpful to obtain some analytical methods of Classical Network Theory, I started to learn about it several months ago and began to form some preparatory ideas and plans recently.

Will it be possible to work out a procedure following which a universal quantum communication network consisting of an arbitrary number of nodes in a general geometry, no matter what kind of qubits is used, can be constituted?

To achieve this aim, it will be useful to absorb some knowledge from Network Theory, since the problems of increasing nodes and establishing links between them also exist in Network Theory. The macroscopic principle of enlarging a quantum network scale might be set up similarly to that of a classical one. For example, starting from an EPR state, it might be able to extend the scale of a quantum network according to the classical network models, to set up a regular quantum network or completely random quantum network by using maximized entangled states, or to get a scale-free quantum network using not fully entangled states, or even to obtain a LW quantum network etc.. However, the microscopic principle of establishing links between nodes in quantum and classical networks will be very different, since the links in the latter one are purely classical and can be fixed artificially, while the links in quantum networks are relatively variable since once a node is entangled with another one, it will definitely share part of the entanglement at the same time when the second qubit is entangled with a third one. Moreover, we have to describe the probability of attachment with density matrix . These are some of the problems we have to take into account when trying to establish a quantum network. Not so much work has been done from a network perspective in this area. The paper Entanglement Percolation in Quantum Networks published on Nature recently showed some two dimensional examples of quantum networks with special topological structures and analyzed their percolation protocols using quantum repeaters.

The second step, after accomplishing the first one, is to analyze the features of quantum networks versus classical ones. How can we evaluate whether a quantum network is good or not? I always keep thinking about this question. Can we define some parameters paralleling to those in classical Network theory, such as the average path length L, degree distribution function P(k) and clustering coefficient C etc. with necessary modifications to describe the basic properties of a quantum network? How can we analyze the robustness and error tolerance of a quantum network, and how much classical and non-classical resources are needed to transfer information in a quantum network? Since the networks studies by network science abound, will it be possible to find a general network theory that covers both the classical and quantum situations, as physicists always keep trying to unify different kinds of interactions under one theory? It might be helpful to analyze the statistical properties of these networks under diverse scales and finally try to make their properties convertible, as I think a comprehensive network theory should be applicable to physical systems of arbitrary scales.

Thanks for reading and giving some suggestions:)

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# Quantum Network and Quantum Imaging

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