Editing Routing Entanglement in the Quantum Internet (section)

===Protocol for Simultaneous Entanglement Flows with Link-state Information===
'''Input:''' <math>K=2</math>, Source-Destination pairs <math>(A_1, B_1)</math> and <math>(A_2, B_2)</math>.

'''Output:''' Quantum network with ebits shared between the end points of <math>(A_1, B_1)</math> and <math>(A_2, B_2)</math>.

This situation motivates the '''Multi-ﬂow Spatial-division''' rule which divides the the network between two spatial regions corresponding to the two flows.

* When the shortest path connecting the two source-destination pairs '''do not''' cross the network is divided between two spatial regions corresponding to the two ﬂows.
** For each one of this regions we apply the Protocol for Entanglement Routing with Local Link-state Information.

* When the shortest path connecting the two source-destination pairs '''do''' cross the network is divided between two spatial regions corresponding to the two ﬂows.
** Considering the square-grid topology the two spatial regions are divided by two crossing lines with an angle <math>\theta</math> between them (forming a hourglass shape).
** For each one of this regions we apply the Protocol for Entanglement Routing with Local Link-state Information.