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BB84 Quantum Key Distribution: Difference between revisions
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** requires [[synchronous network]], [[authenticated]] public classical channel, secure from [[coherent attacks]] | ** requires [[synchronous network]], [[authenticated]] public classical channel, secure from [[coherent attacks]] | ||
** implements <math>(n,\epsilon_{\rm corr},\epsilon_{\rm sec},\ell)</math>-QKD, which means that it generates an <math>\epsilon_{\rm corr}</math>-correct, <math>\epsilon_{\rm sec}</math>-secret key of length <math>\ell</math> in <math>n</math> rounds. The security parameters of this protocol are give by | ** implements <math>(n,\epsilon_{\rm corr},\epsilon_{\rm sec},\ell)</math>-QKD, which means that it generates an <math>\epsilon_{\rm corr}</math>-correct, <math>\epsilon_{\rm sec}</math>-secret key of length <math>\ell</math> in <math>n</math> rounds. The security parameters of this protocol are give by | ||
<math>\epsilon_{\rm corr} | <math>\epsilon_{\rm corr}=\epsilon_{\rm EC},</br> | ||
\epsilon_{\rm sec} | \epsilon_{\rm sec}= \epsilon_{\rm PA}+\epsilon_{\rm PE},</math> | ||
</math> | and the amount of key <math>\ell</math> that is generated is given by</br> | ||
and the amount of key <math>\ell</math> that is generated is given by | <math>\ell\geq (1-\gamma)^2n (1-h(Q_X+\nu) -h(Q_Z))</math></br><math>-\sqrt{(1-\gamma)^2n}\big(4\log(2\sqrt{2}+1)(\sqrt{\log\frac{2}{\epsilon_{\rm PE}^2}}+ \sqrt{\log \frac{8}{{\epsilon'}_{\rm EC}^2}}))</math></br> | ||
<math>\ell\geq | <math>-\log(\frac{8}{{\epsilon'}_{\rm EC}^2}+\frac{2}{2-\epsilon'_{\rm EC}})-\log (\frac{1}{\epsilon_{\rm EC}})- 2\log(\frac{1}{2\epsilon_{\rm PA}})</math></br>where<math>\nu = \sqrt{ \frac{(1+\gamma^2n)((1-\gamma)^2+\gamma^2)}{(1-\gamma)^2\gamma^4n^2}\log(\frac{1}{\epsilon_{\rm PE}}})</math> | ||
where | |||
<math> | |||
\nu = \sqrt{ \frac{(1+\gamma^2n)((1-\gamma)^2+\gamma^2)}{(1-\gamma)^2\gamma^4n^2}\log | |||
and <math>h(\cdot)</math> is the [[binary entropy function]]. | and <math>h(\cdot)</math> is the [[binary entropy function]]. | ||