Device-Independent Quantum Key Distribution: Difference between revisions

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.  

*'''Distribution:''' For each round of the distribution phase:

** Sender uses the source to prepare a maximally entangled state and send half of the state to Receiver.

** 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.

*  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.

* 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.

* Distribution of Bell pairs, and measurement in three different bases (two basis on Sender's side and three basis on Receiver's side).

==Notations Used==

==Pseudo Code==

### Sender and Receiver choose a random bit <math>T_i \in \{0,1\}</math> such that <math>P(T_i=1)=\gamma</math>.

### Sender and Receiver use their devices with the respective inputs and record their outputs, <math>A_i</math> and <math>B_i</math> respectively.

*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>.

* Sender and Receiver apply the error correction protocol <math>EC</math>, communicating script <math>O_{EC}</math> in the process.  

#Using <math>B_1^n</math> and <math>\tilde{B}_1^n</math>, Receiver sets <math>C_i</math>

# Sender and Receiver run <math>PA(A_1^{n'},\tilde{B}_1^{n'})</math> and obtain secret keys <math>K_A, K_B</math>;

<div style='text-align: right;'>''*contributed by Bas Dirke, Victoria Lipinska, Glaucia Murta and Jeremy Ribeiro''</div>