Write
262
edits
BB84 Quantum Key Distribution: Difference between revisions
→Pseudocode
| Line 65: | Line 65: | ||
## Bob chooses bit <math>Y_i\in_R\{0,1\}</math> such that <math>P(Y_i=1)=\gamma</math> | ## Bob chooses bit <math>Y_i\in_R\{0,1\}</math> such that <math>P(Y_i=1)=\gamma</math> | ||
## Bob 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> | ## Bob 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 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.''' Sifting | '''2.''' Sifting | ||
#Alice and Bob publicly announce <math>X_1^n, Y_1^n</math> | #Alice and Bob publicly announce <math>X_1^n, Y_1^n</math> | ||
| Line 75: | Line 75: | ||
### <math>X_1^{n'} = X_1^{n'}.</math>append<math>(X_i)</math> | ### <math>X_1^{n'} = X_1^{n'}.</math>append<math>(X_i)</math> | ||
### <math>Y_1^{n'} = Y_1^{n'}.</math>append<math>(Y_i)</math> | ### <math>Y_1^{n'} = Y_1^{n'}.</math>append<math>(Y_i)</math> | ||
''Now 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'\leq n</math>.'' | |||
'''3.''' Parameter estimation | '''3.''' Parameter estimation | ||
#For <math>i=1,...,n'</math> | #For <math>i=1,...,n'</math> | ||
| Line 83: | Line 84: | ||
### Alice and Bob compute <math>Q_i = 1 - \delta_{A_iB_i}</math>, where <math>\delta_{A_iB_i}</math> is the Kronecker delta | ### Alice and Bob compute <math>Q_i = 1 - \delta_{A_iB_i}</math>, where <math>\delta_{A_iB_i}</math> is the Kronecker delta | ||
## size<math>Q</math> += 1; | ## size<math>Q</math> += 1; | ||
#Both Alice and Bob, each, compute <math>Q_X = \frac{1}{\text{size}Q} \sum_{i=1}^{n'}Q_i</math></br> | |||
'''4.''' 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> | |||
#Both Alice and Bob run <math>C(A_1^{n'},B_1^{n'})</math>''. | #Both Alice and Bob run <math>C(A_1^{n'},B_1^{n'})</math>''. | ||
#Bob obtains <math>\tilde{B}_1^{n'}</math> | #Bob obtains <math>\tilde{B}_1^{n'}</math> | ||
'''5.''' Privacy amplification | '''5.''' Privacy amplification | ||
''<math>PA(\cdot,\cdot)</math> is a privacy amplification subroutine determined by the size <math>\ell</math>, computed from equation for key length <math>\ell</math> (see [[Quantum Key Distribution#Properties|Properties]]), and with secrecy parameter <math>\epsilon_{\rm PA}</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>; | #Alice and Bob run <math>PA(A_1^{n'},\tilde{B}_1^{n'})</math> and obtain secret keys <math>K_A, K_B</math>; | ||