### Distributed quantum algorithms for efficiently generating multipartite entangled states over quantum networks

2018.02.14

Mio Murao, The University of Tokyo

A tree-type cluster quantum computer is a quantum network represented by a tree graph where the nodes are quantum computers. We constructed distributed quantum algorithms for generating an arbitrary multipartite entangled state shared between nodes with a tree-type cluster quantum computer with the minimum amount of quantum communication. In this algorithm, the optimal combination of quantum computation at each node and quantum communication between nodes is chosen based on the decomposition of the target multipartite state customized by the shape of the network. The target state is generated by extending the state part by part at each node for the next forward neighbor. The algorithm also reduces the largest quantum memory space required at the nodes. This research also proposes a new multipartite entanglement measure that has an operational meaning in transforming a collection of bipartite entangled states distributed according to a given quantum network into a multipartite entangled state. We studied approximate generations of multipartite entangled states using block coding to understand this new multipartite entanglement measure from an information theoretical point of view. We have found characteristic properties of multipartite entanglement with a second-order asymptotic analysis of the measure.

Ref: H. Yamasaki, A. Soeda and M. Murao, Phys. Rev. A 96, 032330 (2017)

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