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Device-Independent Quantum Key Distribution: Difference between revisions
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Device-Independent Quantum Key Distribution (edit)
Revision as of 23:32, 18 March 2019
, 18 March 2019→Properties
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Either Protocol (see [[Device Independent Quantum Key Distribution#Pseudo-code|Pseudo-code]]) abort with probability higher than <math>1-(\epsilon_{EA}+\epsilon_{EC})</math>, or it generates a</br> | Either Protocol (see [[Device Independent Quantum Key Distribution#Pseudo-code|Pseudo-code]]) abort with probability higher than <math>1-(\epsilon_{EA}+\epsilon_{EC})</math>, or it generates a</br> | ||
<math>(2\epsilon_{EC}+\epsilon_{PA}+\epsilon_s)</math>-correct-and-secret key of length</br> | <math>(2\epsilon_{EC}+\epsilon_{PA}+\epsilon_s)</math>-correct-and-secret key of length</br> | ||
<math>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}</math></br><math> | <math>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}</math></br> | ||
<math>-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)</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 Table 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 in Protocol 1 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 in Protocol 1 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>. | ||