Device-Independent Quantum Key Distribution: Difference between revisions

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### '''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).
### Alice and Bob use their devices with the respective inputs and record their outputs, <math>A_i</math> and <math>B_i</math> respectively.
### Alice and Bob 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>.</br>
*''At this point 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 point 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>.''


'''2.''' Error Correction</br>
'''2.''' Error Correction
* ''Alice and Bob apply the error correction protocol <math>EC</math>, communicating script <math>O_{EC}</math> in the process. ''
 
''Alice and Bob 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
# '''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>.
# '''Else''' they obtain raw keys <math>\tilde{A}_1^n</math> and <math>\tilde{B}_1^n</math>.
'''3.''' Parameter estimation</br>
'''3.''' Parameter estimation
 
#Using <math>B_1^n</math> and <math>\tilde{B}_1^n</math>, Bob sets <math>C_i</math>
#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=1</math>  
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## '''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>
## '''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 (\omega_{exp}-\delta_{est})(1-(1-\gamma)^{s_{\max}})</math>, i.e., if they do not achieve the expected violation.  
# He aborts '''If''' <math>\sum_j C_{j}<m\times (\omega_{exp}-\delta_{est})(1-(1-\gamma)^{s_{\max}})</math>, i.e., if they do not achieve the expected violation.  
'''4.''' Privacy amplification</br>
 
*<math>PA(\cdot,\cdot)</math> ''is a privacy amplification subroutine''
'''4.''' Privacy amplification
 
<math>PA(\cdot,\cdot)</math> ''is a privacy amplification subroutine''
# Alice and Bob run <math>PA(A_1^{n'},\tilde{B}_1^{n'})</math> and obtain secret keys <math>K_A, K_B</math>;
# Alice and Bob run <math>PA(A_1^{n'},\tilde{B}_1^{n'})</math> and obtain secret keys <math>K_A, K_B</math>;


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