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Device-Independent Quantum Key Distribution (edit)
Revision as of 13:13, 19 March 2019
, 19 March 2019→Pseudo Code
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##'''While''' <math>i \leq s_{max}</math> | ##'''While''' <math>i \leq s_{max}</math> | ||
###Set <math>i=i+1</math> | ###Set <math>i=i+1</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>. | ### '''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). | ### '''Else''' they choose <math>X_i ,Y_i \in \{0,1\}</math> (the observables for the CHSH test). | ||
### | ### 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>. | ### '''If''' <math>T_i=1</math> they set <math>i=s_{max}+1</math>. | ||
*At this stage | *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> | <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 4'''</u> Error correction | ||
<u>'''Stage 5'''</u> Privacy amplification | <u>'''Stage 5'''</u> Privacy amplification | ||
==Further Information== | ==Further Information== | ||