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Device-Independent Quantum Key Distribution: Difference between revisions
Device-Independent Quantum Key Distribution (edit)
Revision as of 10:22, 25 April 2019
, 25 April 2019→Pseudocode
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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>.'' | |||
'''2.''' Error Correction | '''2.''' Error Correction | ||
''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 | '''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 | |||
'''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>; | ||