Figure 1

The schematic model of the resource consumption evaluation of a quantum repeater \(R_{i} \) in a quantum Internet scenario. The quantum repeater has z incoming entangled connections, \({\mathrm{L}}_{l} \left( k\right) \), \(k=1,\ldots ,z\), from among \(\left| {{\mathscr {S}}}_{{\mathscr {P}}} \left( R_{i} \right) \right| =2\) paths, \({{\mathscr {P}}}_{s} \left( A,B\right) \), \(s=1,2\), that pass through quantum repeater \(R_{i} \) between A and B. The paths \({{\mathscr {P}}}_{1} \left( A,B\right) \) and \({{\mathscr {P}}}_{2} \left( A,B\right) \) are associated with the weighted entanglement throughput values \(\omega \left( {{\mathscr {P}}}_{1} \left( A,B\right) \right) B_{F} \left( {{\mathscr {P}}}_{s} \left( A\right) \right) \) and \(\omega \left( {{\mathscr {P}}}_{2} \left( A,B\right) \right) B_{F} \left( {{\mathscr {P}}}_{s} \left( A\right) \right) \), where \(\omega \left( {{\mathscr {P}}}_{s} \left( A,B\right) \right) \in \left[ 0,1\right] \) are the path weights and \(B_{F} \left( {{\mathscr {P}}}_{s} \left( A\right) \right) \) is the entanglement throughput (Bell states per C) of the source A of the path \({{\mathscr {P}}}_{s} \). (The entangled states associated with the entangled connections in the quantum repeater are depicted by green, brown, and black dots.)