Editing Device-Independent Quantum Key Distribution
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'''Tags:''' [[:Category:Two Party Protocols|Two Party]], [[:Category:Quantum Enhanced Classical Functionality|Quantum Enhanced Classical Functionality]], [[:Category:Specific Task|Specific Task]],[[Quantum Key Distribution]], [[BB84 Quantum Key Distribution|BB84 QKD]], [[Category:Multi Party Protocols]] [[Category:Quantum Enhanced Classical Functionality]][[Category:Specific Task]][[Category:Entanglement Distribution Network | A device-independent quantum key distribution protocol implements the task of [[Quantum Key Distribution]] (QKD) without relying on any particular description of the underlying system. The protocol enables two parties, Alice and Bob, to establish a classical secret key by distributing an entangled quantum state and checking for the violation of a [[Bell inequality]] in order to certify the security. The output of the protocol is a classical secret key which is completely unknown to any third party, namely an eavesdropper. | ||
'''Tags:''' [[:Category:Two Party Protocols|Two Party]], [[:Category:Quantum Enhanced Classical Functionality|Quantum Enhanced Classical Functionality]], [[:Category:Specific Task|Specific Task]],[[Quantum Key Distribution]], [[BB84 Quantum Key Distribution|BB84 QKD]], [[Category:Multi Party Protocols]] [[Category:Quantum Enhanced Classical Functionality]][[Category:Specific Task]][[Category:Entanglement Distribution Network Stage]] | |||
==Assumptions== | ==Assumptions== | ||
* '''Network:''' we assume the existence of an authenticated public classical channel between Alice and Bob. | * '''Network:''' we assume the existence of an authenticated public classical channel between Alice and Bob. | ||
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* In the final phase, Alice and Bob perform [[privacy amplification]], where the not fully secure <math>n</math>-bit strings are mapped into smaller strings <math>K_A</math> and <math>K_B</math>, which represents the final keys of Alice and Bob respectively. | * In the final phase, Alice and Bob perform [[privacy amplification]], where the not fully secure <math>n</math>-bit strings are mapped into smaller strings <math>K_A</math> and <math>K_B</math>, which represents the final keys of Alice and Bob respectively. | ||
==Requirements == | ==Hardware Requirements == | ||
*'''Network Stage:''' [[:Category:Entanglement Distribution Network | *'''Network Stage:''' [[:Category: Entanglement Distribution Network Stage|Entanglement Distribution]] | ||
*'''Relevant Network Parameters:''' | *'''Relevant Network Parameters:''' <math>\epsilon_T, \epsilon_M</math> (see [[:Category: Entanglement Distribution Network Stage|Entanglement Distribution]]). | ||
*'''Benchmark values:''' | *'''Benchmark values:''' | ||
** Minimum number of rounds ranging from <math>\mathcal{O}(10^6)</math> to <math>\mathcal{O}(10^{12})</math> depending on the network parameters | ** Minimum number of rounds ranging from <math>\mathcal{O}(10^6)</math> to <math>\mathcal{O}(10^{12})</math> depending on the network parameters, for commonly used secure parameters. | ||
** <math>QBER \leq 0.071</math>, taking a depolarizing model as benchmark. Parameters satisfying <math>\epsilon_T+\epsilon_M\leq 0.071</math> are sufficient | ** <math>QBER \leq 0.071</math>, taking a depolarizing model as benchmark. Parameters satisfying <math>\epsilon_T+\epsilon_M\leq 0.071</math> are sufficient. | ||
* Distribution of Bell pairs, and measurement in three different bases (two basis on Alice's side and three basis on Bob's side). | * Distribution of Bell pairs, and measurement in three different bases (two basis on Alice's side and three basis on Bob's side). | ||
* Requires [[random number generator]]. | * Requires [[random number generator]]. | ||
==Notation== | ==Notation== | ||
* <math>n</math> expected number of rounds | * <math>n</math> expected number of rounds | ||
* <math>l</math> final key length | * <math>l</math> final key length | ||
* <math>\gamma</math> fraction of test rounds | * <math>\gamma</math> fraction of test rounds | ||
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* <math>\epsilon_{PA}</math> error probability of the privacy amplification protocol | * <math>\epsilon_{PA}</math> error probability of the privacy amplification protocol | ||
* <math>\mbox{leak}_{EC}</math> leakage in the error correction protocol | * <math>\mbox{leak}_{EC}</math> leakage in the error correction protocol | ||
==Properties== | ==Properties== | ||
Either the protocol (see [[Device Independent Quantum Key Distribution#Pseudocode|Pseudocode]]) aborts with probability higher than <math>1-(\epsilon_{EA}+\epsilon_{EC})</math>, or it generates a</br> | Either the protocol (see [[Device Independent Quantum Key Distribution#Pseudocode|Pseudocode]]) aborts with probability higher than <math>1-(\epsilon_{EA}+\epsilon_{EC})</math>, or it generates a</br> | ||
<math>(2\epsilon_{EC}+\epsilon_{PA}+\epsilon_s)</math>-correct-and-secret key of length | <math>(2\epsilon_{EC}+\epsilon_{PA}+\epsilon_s)</math>-correct-and-secret key of length</br> | ||
<math> | <math> | ||
\begin{align} | \begin{align} | ||
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*<math>\nu_1=2 \Big(\log 7 +\left\lceil\frac{|h'(\omega_{exp}+\delta_{est})|}{1-(1-\gamma)^{s_{\max}}}\right\rceil\Big)\sqrt{1-2\log\epsilon_s}</math> | *<math>\nu_1=2 \Big(\log 7 +\left\lceil\frac{|h'(\omega_{exp}+\delta_{est})|}{1-(1-\gamma)^{s_{\max}}}\right\rceil\Big)\sqrt{1-2\log\epsilon_s}</math> | ||
== | ==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> | ||
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### Alice and Bob choose a random bit <math>T_i \in \{0,1\}</math> such that <math>P(T_i=1)=\gamma</math>. | ### Alice and Bob choose a random bit <math>T_i \in \{0,1\}</math> such that <math>P(T_i=1)=\gamma</math>. | ||
### '''If''' <math>T_i=0</math> '''then''' Alice and Bob choose inputs <math>(X_i, Y_i)=(0,2)</math>. | ### '''If''' <math>T_i=0</math> '''then''' Alice and Bob choose inputs <math>(X_i, Y_i)=(0,2)</math>. | ||
### '''Else''' they choose <math>X_i ,Y_i \in \{0,1\}</math>. | ### '''Else''' they choose <math>X_i ,Y_i \in \{0,1\}</math> (the observables for the CHSH test). | ||
### 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>.</br> | ### '''If''' <math>T_i=1</math> they set <math>i=s_{max}+1</math>.</br> | ||
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##'''If''' <math>T_i=1</math> and <math>A_i\oplus B_i\neq X_i\cdot Y_i</math> '''then''' <math>C_i=0</math> | ##'''If''' <math>T_i=1</math> and <math>A_i\oplus B_i\neq X_i\cdot Y_i</math> '''then''' <math>C_i=0</math> | ||
## '''If''' <math>T_i=0</math> '''then''' <math>C_i=\bot</math> | ## '''If''' <math>T_i=0</math> '''then''' <math>C_i=\bot</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. | ||
''For the summation in 3.2 we use the convention that <math>\forall x\in \{0,1,\bot\},\ x+\bot=\bot+x=x</math>, that is <math>\bot</math> acts as <math>0</math> with respect to the addition.'' | ''For the summation in 3.2 we use the convention that <math>\forall x\in \{0,1,\bot\},\ x+\bot=\bot+x=x</math>, that is <math>\bot</math> acts as <math>0</math> with respect to the addition.'' | ||
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#[https://doi.org/10.1007/3-540-48285-7_35 Secret-Key Reconciliation by Public Discussion] | #[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] | #[https://arxiv.org/abs/quant-ph/0512258 Security of Quantum Key Distribution] | ||
<div style='text-align: right;'>''contributed by Gláucia Murta''</div> | <div style='text-align: right;'>''contributed by Gláucia Murta''</div> |