Editing Distributing Graph States Over Arbitrary Quantum Networks (section)

==Outline==
The protocol [https://arxiv.org/abs/1811.05445 (1)] aims to distribute multipartite entangled states that are represented by graph states over fixed networks of arbitrary topology. They first introduce a protocol to distribute GHZ states that considering the assumptions takes a single time step and is optimal in terms of the Bell pair used. Their second protocol is a generalization of the first one and can distribute any arbitrary graph state using at most twice as many Bell pairs and steps than the optimal distributing protocol for the worst case scenario.

In this protocol a quantum network is represented as a graph
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The physical distribution of graph states are represented as graph operations ignoring
local corrections.


To distribute a '''GHZ states''' over all the nodes of an arbitrary set <math>W</math> of the network nodes we have two steps:

# Find a minimal tree covering all the nodes of <math>W</math> using the [https://en.wikipedia.org/wiki/Steiner_tree_problem Steiner Tree Problem].
#* Minimal tree is a subgraph connecting all the nodes in <math>W</math> with the minimum number of edges.
# Apply an operation called Star Expansion on the leaves of the tree from the previous step.
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To distribute an '''Arbitrary Graph State''' we realize multiple iterations of the protocol above. 
After that we make measurements on the participating nodes to generate the arbitrary graph state we want.
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