Device-Independent Quantum Key Distribution: Difference between revisions

Device-Independent Quantum Key Distribution (edit)

Revision as of 13:13, 19 March 2019

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 ##'''While''' <math>i \leq s_{max}</math>
 ###Set <math>i=i+1</math>
-### Alice and Bob choose a random bit <math>T_i \in \{0,1\}</math> such that <math>P(T_i=1)=\gamma</math>.
+### Sender and Receiver choose a random bit <math>T_i \in \{0,1\}</math> such that <math>P(T_i=1)=\gamma</math>.
 ### '''If''' <math>T_i=0</math> '''then''' Alice and Bob choose inputs <math>(X_i, Y_i)=(0,2)</math>.
 ### '''Else''' they choose  <math>X_i ,Y_i \in \{0,1\}</math>  (the observables for the CHSH test).
-### Alice and Bob use their devices with the respective inputs and record their outputs, <math>A_i</math> and <math>B_i</math> respectively.
+### Sender and Receiver use their devices with the respective inputs and record their outputs, <math>A_i</math> and <math>B_i</math> respectively.
 ### '''If''' <math>T_i=1</math> they  set <math>i=s_{max}+1</math>.
-*At this stage Alice holds strings <math>X_1^n, A_1^n</math> and Bob <math>Y_1^n, B_1^n</math>, all of length <math>n</math>.
+*At this stage Sender holds strings <math>X_1^n, A_1^n</math> and Receiver <math>Y_1^n, B_1^n</math>, all of length <math>n</math>.
-<u>'''Stage 2'''</u> Sifting
+<u>'''Stage 2'''</u> Error Correction</br>
-<u>'''Stage 3'''</u> Parameter estimation
+* Sender and Receiver apply the error correction protocol <math>EC</math>, communicating script <math>O_{EC}</math> in the process.
+# '''If''' <math>EC</math> aborts they abort the protocol
+# '''Else''' they obtain raw keys <math>\tilde{A}_1^n</math> and <math>\tilde{B}_1^n</math>.
+<u>'''Stage 3'''</u> Parameter estimation</br>
+#Using <math>B_1^n</math> and <math>\tilde{B}_1^n</math>, Bob sets <math>C_i</math>
+##'''If''' <math>T_i=1</math>  and <math>A_i\oplus B_i=X_i\cdot Y_i</math> '''then''' <math>C_i=1</math>
+##'''If''' <math>T_i=1</math>  and <math>A_i\oplus B_i=X_i\cdot Y_i</math> '''then''' <math>C_i=0</math>
+## '''If''' <math>T_i=1</math>  and <math>A_i\oplus B_i=X_i\cdot Y_i</math> '''then''' <math>C_i=\bot</math>
+#He aborts '''If''' <math>\sum_j C_j<m\times \Bigg(\omega_{exp}-\delta_{est}}(1-(1-\gamma)^{s_{\max}\Bigg))
+*\textit{i.e.}, if they do not achieve the expected violation.
 <u>'''Stage 4'''</u> Error correction
 <u>'''Stage 5'''</u> Privacy amplification
 ==Further Information==