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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 17:03, 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> | '''1.''' Distribution and measurement</br> | ||
#'''For''' every block <math> j \in [m]</math> | #'''For''' every block <math> j \in [m]</math> | ||
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### 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>. | ||
*At this | *''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</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>. | ||
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# 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> | '''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>; | ||