Write
262
edits
BB84 Quantum Key Distribution: Difference between revisions
no edit summary
No edit summary |
|||
| Line 88: | Line 88: | ||
'''4.''' Error correction | '''4.''' Error correction | ||
''<math>C(\cdot,\cdot)</math> is an error correction subroutine (see [[BB84 Quantum Key Distribution #References| [ | ''<math>C(\cdot,\cdot)</math> is an error correction subroutine (see [[BB84 Quantum Key Distribution #References| [9]]]) 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>'' | ''<math>PA(\cdot,\cdot)</math> is a privacy amplification subroutine (see [[BB84 Quantum Key Distribution #References| [10]]]) 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>; | ||
| Line 102: | Line 102: | ||
# Sifting: the BB84 protocol can also be described in a symmetric way. This means that the inputs <math>0</math> and <math>1</math> are chosen with the same probability. In that case only <math>1/2</math> of the generated bits are discarded during the sifting process. Indeed, in the symmetric protocol, Alice and Bob measure in the same basis in about half of the rounds. | # Sifting: the BB84 protocol can also be described in a symmetric way. This means that the inputs <math>0</math> and <math>1</math> are chosen with the same probability. In that case only <math>1/2</math> of the generated bits are discarded during the sifting process. Indeed, in the symmetric protocol, Alice and Bob measure in the same basis in about half of the rounds. | ||
# [https://dl.acm.org/citation.cfm?id=1058094 LCA05] the asymmetric protocol was introduced to make this more efficient protocol presented in this article. | # [https://dl.acm.org/citation.cfm?id=1058094 LCA05] the asymmetric protocol was introduced to make this more efficient protocol presented in this article. | ||
# A post-processing of the key using 2-way classical communication, denoted [[Advantage distillation]], can increase the QBER | # A post-processing of the key using 2-way classical communication, denoted [[Advantage distillation]], can increase the QBER tolerance up to <math>18.9\%</math> (3). | ||
# We remark that in [[BB84 Quantum Key Distribution#Pseudo Code|Pseudo Code]], the QBER in the <math>Z</math> basis is not estimated during the protocol. Instead Alice and Bob make use of a previous estimate for the value of <math>Q_Z</math> and the error correction step, Step 4 in the pseudo-code, will make sure that this estimation is correct. Indeed, if the real QBER is higher than the estimated value <math>Q_Z</math>, [[BB84 Quantum Key Distribution#Pseudo Code|Pseudo Code]] will abort in the Step 4 with very high probability. | # We remark that in [[BB84 Quantum Key Distribution#Pseudo Code|Pseudo Code]], the QBER in the <math>Z</math> basis is not estimated during the protocol. Instead Alice and Bob make use of a previous estimate for the value of <math>Q_Z</math> and the error correction step, Step 4 in the pseudo-code, will make sure that this estimation is correct. Indeed, if the real QBER is higher than the estimated value <math>Q_Z</math>, [[BB84 Quantum Key Distribution#Pseudo Code|Pseudo Code]] will abort in the Step 4 with very high probability. | ||
# The BB84 can be equivalently implemented by distributing [[EPR pairs]] and Alice and Bob making measurements in the <math>Z</math> and <math>X</math> basis, however this required a [[entanglement distribution]] network stage. | # The BB84 can be equivalently implemented by distributing [[EPR pairs]] and Alice and Bob making measurements in the <math>Z</math> and <math>X</math> basis, however this required a [[entanglement distribution]] network stage. | ||
#[https://doi.org/10.1007/3-540-48285-7_35 Secret-Key Reconciliation by Public Discussion] | |||
#[https://arxiv.org/abs/quant-ph/0512258 Security of Quantum Key Distribution] | |||
<div style='text-align: right;'>''contributed by Bas Dirke, Victoria Lipinska, Gláucia Murta and Jérémy Ribeiro''</div> | <div style='text-align: right;'>''contributed by Bas Dirke, Victoria Lipinska, Gláucia Murta and Jérémy Ribeiro''</div> | ||