Device-Independent Quantum Key Distribution: Difference between revisions

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<math>
<math>
\begin{align}
\begin{align}
l\geq &\frac{{n}}{\bar{s}}\eta_{opt} -\frac{{n}}{\bar{s}}h(\omega_{exp}-\delta_{est}) -\sqrt{\frac{{n}}{\bar{s}}}\nu_1  -\mbox{leak}_{EC} \\
l\geq \frac{{n}}{\bar{s}}\eta_{opt} -\frac{{n}}{\bar{s}}h(\omega_{exp}-\delta_{est}) -\sqrt{\frac{{n}}{\bar{s}}}\nu_1  -\mbox{leak}_{EC} -3\log\Bigg(1-\sqrt{1-\Bigg(\frac{\epsilon_s}{4(\epsilon_{EA} + \epsilon_{EC})}\Bigg)^2}\Bigg)+2\log\Bigg(\frac{1}{2\epsilon_{PA}}\Bigg),
& -3\log\Bigg(1-\sqrt{1-\Bigg(\frac{\epsilon_s}{4(\epsilon_{EA} + \epsilon_{EC})}\Bigg)^2}\Bigg)+2\log\Bigg(\frac{1}{2\epsilon_{PA}}\Bigg)
\end{align}
\end{align}
</math>,</br>
</math></br>
where <math>\mbox{leak}_{EC}</math> is the leakage due to error correction step and the functions <math>\bar{s}</math>, <math>\eta_{opt}</math>, <math>\nu_1</math> and <math>\nu_2</math> are specified in below.
where <math>\mbox{leak}_{EC}</math> is the leakage due to error correction step and the functions <math>\bar{s}</math>, <math>\eta_{opt}</math>, <math>\nu_1</math> and <math>\nu_2</math> are specified in below.
The security parameters of the error correction protocol, <math>\epsilon_{EC}</math> and <math>\epsilon'_{EC}</math>, mean that if the error correction step of the protocol (see below) does not abort, then <math>K_A=K_B</math> with probability at least <math>1-\epsilon_{EC}</math>, and for an honest implementation, the error correction protocol aborts with probability at most <math>\epsilon'_{EC}+\epsilon_{EC}</math>.
The security parameters of the error correction protocol, <math>\epsilon_{EC}</math> and <math>\epsilon'_{EC}</math>, mean that if the error correction step of the protocol (see below) does not abort, then <math>K_A=K_B</math> with probability at least <math>1-\epsilon_{EC}</math>, and for an honest implementation, the error correction protocol aborts with probability at most <math>\epsilon'_{EC}+\epsilon_{EC}</math>.
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