Editing Distributed Routing in a Quantum Internet (section)

==Notation==
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* Quantum network with topology described by two graphs:
* A '''physical''' graph <math>G_{ph}=(V,E_{ph})</math>
** <math>V</math> represent quantum repeater nodes that can hold a small number of qubits.
** <math>E_{ph}</math> correspond to physical communication channels between nodes.
* A '''virtual''' graph <math>\mathcal{G}=(V,\mathcal{E})</math>
** <math>\mathcal{E}</math> represent ''virtual links'', nodes that are not physically connected but share entanglement.
* <math>D</math> is a <math>|V|\times|V|</math> matrix representing the demands
** <math>D_{i,j}</math> denotes the number of entangled links the source node <math>i \in V</math> wants to share with destination node <math>j \in V</math> at a specific point in time.
* <math>cap</math> denotes the maximum number of entangled links any two neighbour nodes <math>u</math> and <math>v</math> can share simultaneously.
* The ''average latency (AL)'' is defined as:
* <math>AL = \frac{1}{|D|} \sum_{i,j} T_{A,i,j}</math>, where
** <math>|D|</math>  denotes the number of non-zero entries in <math>D</math>
** <math>T_{A,i,j}</math> denotes the latency that a routing algorithm <math>\mathcal{A}</math> takes to distribute <math>D_{i,j}</math> entangled link between the nodes <math>i</math> and <math>j</math>.

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