Figure 6
From: Resource prioritization and balancing for the quantum internet
(a) Comparison of the amounts of traffic \(T\left( {{\mathscr {S}}}_{n_{c} } ,{{{\mathscr {M}}}}\right) \) and \(B\left( {{\mathscr {S}}}_{n_{c} } ,{{\mathscr {S}}}_{{\mathscr {N}}} \right) \) (Bell states per C) within the structures of \({{{\mathscr {M}}}}\) and \({{\mathscr {S}}}_{{\mathscr {N}}} \), with \(T\left( x_{I}^{\left( {{{\mathscr {M}}}}\right) } ,S_{i}^{n_{c} } \right) =B\left( R_{q}^{\left( {{\mathscr {S}}}_{{\mathscr {N}}} \right) } ,S_{i}^{n_{c} } \right) =100\) and \(\left| {{{\mathscr {M}}}}\right| =\left| {{\mathscr {S}}}_{{\mathscr {N}}} \right| =1,\ldots ,100\). (b) Comparison of the fanout coefficients \({{{\mathscr {F}}}}\left( {{{\mathscr {M}}}}\right) \) and \({{{\mathscr {F}}}}\left( {{\mathscr {S}}}_{{\mathscr {N}}} \right) \) of the structures of \({{{\mathscr {M}}}}\) and \({{\mathscr {S}}}_{{\mathscr {N}}} \), with \(\left| {{{\mathscr {M}}}}\right| =\left| {{\mathscr {S}}}_{{\mathscr {N}}} \right| =1,\ldots ,100\). (c) The entanglement throughput increment \(\Delta _{k} \) (Bell states per C) of the \(\left| E\left( {{\mathscr {S}}}_{{\mathscr {N}}} \right) \right| -k\) entangled connections at the failure of k entangled connections within \({{\mathscr {S}}}_{{\mathscr {N}}} \), with \(k=1,\ldots ,100\), \(\left| {{\mathscr {S}}}_{{\mathscr {N}}} \right| =100\), \(B\left( R_{q}^{\left( {{\mathscr {S}}}_{{\mathscr {N}}} \right) } ,R_{i} \right) =100\), and \(Q\left( R_{q}^{\left( {{\mathscr {S}}}_{{\mathscr {N}}} \right) } ,R_{z}^{\left( {{\mathscr {S}}}_{{\mathscr {N}}} \right) } \right) ={\textstyle \frac{1}{\left| {{\mathscr {S}}}_{{\mathscr {N}}} \right| }} B\left( R_{q}^{\left( {{\mathscr {S}}}_{{\mathscr {N}}} \right) } ,R_{i} \right) =1\), \(Q_{k}^{*} \left( R_{q}^{\left( {{\mathscr {S}}}_{{\mathscr {N}}} \right) } ,R_{z}^{\left( {{\mathscr {S}}}_{{\mathscr {N}}} \right) } \right) \cong {\textstyle \frac{1}{\left| {{\mathscr {S}}}_{{\mathscr {N}}} \right| -k}} B\left( R_{q}^{\left( {{\mathscr {S}}}_{{\mathscr {N}}} \right) } ,{{\mathscr {S}}}_{n_{c} } \right) \). For the comparison between classical resource balancing and quantum resource balancing, the proposed results are compared with the results of135,136.
