Device-Independent Quantum Key Distribution: Difference between revisions

Device-Independent Quantum Key Distribution (edit)

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-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, Sender and Receiver, 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.
+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]]
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 ==Outline==
 A DIQKD protocol is composed by the following steps:
-*'''Distribution:''' For each round of the distribution phase:
+* The first phase of the protocol is the distribution. For each round of this phase:
-** Sender uses the source to prepare a maximally entangled state and send half of the state to Receiver.
+** Alice uses the source to prepare a maximally entangled state and send half of the state to Bob.
-** Upon receiving the state, Receiver announces that he received it, and they both use their respective devices to measure the quantum systems. They record their output in a string of bits.
+** Upon receiving the state, Bob announces that he received it, and they both use their respective devices to measure the quantum systems. They record their output in a string of bits.
-*  A second phase where Sender and Receiver publicly exchange classical information in order to perform [[error correction]], where they correct their strings generating the raw keys, and [[parameter estimation]], where they estimate the parameters of interest. At the end of this phase Sender and Receiver are supposed to share the same <math>n</math>-bit string and have an estimate of how much knowledge an eavesdropper might have about their raw key.
+*  The second phase is when Alice and Bob publicly exchange classical information in order to perform [[error correction]], where they correct their strings generating the raw keys, and [[parameter estimation]], where they estimate the parameters of interest. At the end of this phase Alice and Bob are supposed to share the same <math>n</math>-bit string and have an estimate of how much knowledge an eavesdropper might have about their raw key.
-* In the final phase, Sender and Receiver 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 Sender and Receiver 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.
 ==Hardware Requirements ==
 *'''Network Stage:''' [[:Category: Entanglement Distribution Network Stage|Entanglement Distribution]]
 *'''Relevant Network Parameters:''' <math>\epsilon_T, \epsilon_M</math> (see [[:Category: Entanglement Distribution Network Stage|Entanglement Distribution]])
-* Distribution of Bell pairs, and measurement in three different bases (two basis on Sender's side and three basis on Receiver'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).
 * 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.
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 * [[Random number generator]].
-==Notations Used==
+==Notation==
 * <math>n</math> expected number of rounds
 * <math>l</math> final key length
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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>
-==Pseudo Code==
+==Pseudocode==
 *'''Input:'''<math>n, \delta</math></br>
 *'''Output:'''<math>K_A, K_B</math></br>
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 ##'''While''' <math>i \leq s_{max}</math>
 ###Set <math>i=i+1</math>
-### Sender and Receiver 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>.
 ### '''Else''' they choose  <math>X_i ,Y_i \in \{0,1\}</math>  (the observables for the CHSH test).
-### Sender and Receiver 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>.
-*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 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>.
 <u>'''Stage 2'''</u> Error Correction</br>
-* Sender and Receiver 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
 # '''Else''' they obtain raw keys <math>\tilde{A}_1^n</math> and <math>\tilde{B}_1^n</math>.
 <u>'''Stage 3'''</u> Parameter estimation</br>
-#Using <math>B_1^n</math> and <math>\tilde{B}_1^n</math>, Receiver sets <math>C_i</math>
+#Using <math>B_1^n</math> and <math>\tilde{B}_1^n</math>, Bob sets <math>C_i</math>
 ##'''If''' <math>T_i=1</math>  and <math>A_i\oplus B_i=X_i\cdot Y_i</math> '''then''' <math>C_i=1</math>
 ##'''If''' <math>T_i=1</math>  and <math>A_i\oplus B_i=X_i\cdot Y_i</math> '''then''' <math>C_i=0</math>
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 <u>'''Stage 4'''</u> Privacy amplification</br>
 *<math>PA(\cdot,\cdot)</math> is a privacy amplification subroutine
-# Sender and Receiver 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>;
 ==Further Information==
-<div style='text-align: right;'>''*contributed by Bas Dirke, Victoria Lipinska, Glaucia Murta and Jeremy Ribeiro''</div>
+<div style='text-align: right;'>''contributed by Gláucia Murta''</div>