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BB84 Quantum Key Distribution: Difference between revisions
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<u>'''Stage 1'''</u> Distribution and measurement | <u>'''Stage 1'''</u> Distribution and measurement | ||
#For i=1,2,...,n | #For i=1,2,...,n | ||
## Sender chooses random bits <math>X_i\ | ## Sender chooses random bits <math>X_i\epsilon\{0,1\}</math> and <math>A_i\epsilon_R\{0,1\}</math> such that <math>P(X_i=1)=\gamma</math> | ||
## Sender prepares <math>H^{X_i}\ | ## Sender prepares <math>H^{X_i}|A_i\rangle</math> and sends it to Bob | ||
## Receiver announces receiving a state | ## Receiver announces receiving a state | ||
## Receiver chooses bit <math>Y_i\in_R\{0,1\}</math> such that <math>P(Y_i=1)=\gamma</math> | ## Receiver chooses bit <math>Y_i\in_R\{0,1\}</math> such that <math>P(Y_i=1)=\gamma</math> | ||
## Receiver measures <math>H^{X_i}\ | ## Receiver measures <math>H^{X_i}|A_i\rangle</math> in basis <math>\{H^{Y_i}|0\rangle, H^{Y_i}|1\rangle\}</math> with outcome <math>B_i</math> | ||
*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> | *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> | ||
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#For i=1,2,....,n | #For i=1,2,....,n | ||
## If <math>X_i=Y_i</math> | ## If <math>X_i=Y_i</math> | ||
### <math>A_1^{n'} = A_1^{n'}. | ### <math>A_1^{n'} = A_1^{n'}.</math>append</math>(A_i)</math> | ||
### <math>B_1^{n'} = B_1^{n'}. | ### <math>B_1^{n'} = B_1^{n'}.</math>append<math>(B_i)</math> | ||
### <math>X_1^{n'} = X_1^{n'}. | ### <math>X_1^{n'} = X_1^{n'}.</math>append<math>(X_i)</math> | ||
### <math>Y_1^{n'} = Y_1^{n'}. | ### <math>Y_1^{n'} = Y_1^{n'}.</math>append<math>(Y_i)</math> | ||
*Now 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'\leq n</math> | *Now 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'\leq n</math> | ||
<u>'''Stage 3'''</u> Parameter estimation | <u>'''Stage 3'''</u> Parameter estimation | ||
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## size<math>Q</math> += 1\; | ## size<math>Q</math> += 1\; | ||
Both Sender and Receiver, each, compute <math>Q_X = \frac{1}{\tn{size}Q} \sum_{i=1}^{n'}Q_i</math> | *Both Sender and Receiver, each, compute <math>Q_X = \frac{1}{\tn{size}Q} \sum_{i=1}^{n'}Q_i</math></br> | ||
<u>'''Stage 4'''</u> Error correction | <u>'''Stage 4'''</u> Error correction | ||
<math>C(\cdot,\cdot)</math> is an error correction subroutine determined by the previously estimated value of <math>Q_Z</math> and with error parameters <math>\epsilon'_{\rm EC}</math> and <math>\epsilon_{\rm EC}</math> | #<math>C(\cdot,\cdot)</math> is an error correction subroutine determined by the previously estimated value of <math>Q_Z</math> and with error parameters <math>\epsilon'_{\rm EC}</math> and <math>\epsilon_{\rm EC}</math> | ||
Both Sender and Receiver run <math>C(A_1^{n'},B_1^{n'})</math>. Receiver obtains <math>\tilde{B}_1^{n'}</math> | #Both Sender and Receiver run <math>C(A_1^{n'},B_1^{n'})</math>. | ||
#Receiver obtains <math>\tilde{B}_1^{n'}</math> | |||
<u>'''Stage 5'''</u> Privacy amplification | <u>'''Stage 5'''</u> Privacy amplification | ||
<math>PA(\cdot,\cdot)</math> is a privacy amplification subroutine determined by the size <math>\ell</math>, computed from Eq.(3), and with secrecy parameter <math>\epsilon_{\rm PA}</math> | #<math>PA(\cdot,\cdot)</math> is a privacy amplification subroutine determined by the size <math>\ell</math>, computed from Eq.(3), and with secrecy parameter <math>\epsilon_{\rm PA}</math> | ||
Sender and Receiver run $PA(A_1^{n'},\tilde{B}_1^{n'})$ and obtain secret keys $K_A, K_B$\; | #Sender and Receiver run $PA(A_1^{n'},\tilde{B}_1^{n'})$ and obtain secret keys $K_A, K_B$\; | ||
==Relevant Papers== | ==Relevant Papers== | ||