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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 16:00, 24 April 2019
, 24 April 2019→Pseudocode
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==Pseudocode== | ==Pseudocode== | ||
*'''Input:'''<math>n, \delta</math></br> | *'''Input:'''<math> n, \delta</math></br> | ||
*'''Output:'''<math>K_A, K_B</math></br> | *'''Output:'''<math> K_A, K_B</math></br> | ||
'''1.''' Distribution and measurement</br> | |||
#'''For''' every block <math> j \in [m]</math> | #'''For''' every block <math> j \in [m]</math> | ||
##Set <math>i=0</math> and <math>C_j=\bot</math>. | ##Set <math>i=0</math> and <math>C_j=\bot</math>. | ||
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*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 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> | |||
* 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> | |||
#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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# He aborts '''If''' <math>\sum_j C_{j}<m\times (\omega_{exp}-\delta_{est})(1-(1-\gamma)^{s_{\max}})</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. | * ''i.e.'', if they do not achieve the expected violation. | ||
'''4.''' Privacy amplification</br> | |||
*<math>PA(\cdot,\cdot)</math> is a privacy amplification subroutine | *<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>; | ||