Editing Certified finite randomness expansion (section)

==Outline==

In this protocol, Alice has an initial private random string (the seed) and has been provided with two identical measurement devices by Eve. Each of the devices has two settings and can produce two outputs. Prior to beginning the protocol, Alice has to decide with which confidence she would like her output string to be private from Eve, and which strong randomness extractor she would like to perform post-processing with. She then splits her seed into two portions - the sizes of which are determined by the chosen randomness extractor. 

Alice then takes two bits from the start of the first portion of her initial string and uses these to choose the settings of her measurement devices (i.e. if the pair is <math>(0,1)</math> then she sets the first device to setting $0$ and the second device to setting <math>1</math>). She prepares an [https://wiki.veriqloud.fr/index.php?title=Glossary EPR state] and shares it across the two measurement devices, then performs measurements using each device with the chosen settings and records the output. She repeats this process until this portion of her input string has been exhausted, resulting in a binary string of recorded outputs of equal length to the input.

Using the input and output strings, Alice estimates the violation of the CHSH inequality her experiment has produced. This allows her to place a bound on the [https://wiki.veriqloud.fr/index.php?title=Glossary conditional min-entropy] of the output string with respect to both the input string and any information Eve may have. 

Finally, Alice passes her output string, the second portion of her initial seed and the determined min-entropy bound to a strong randomness extractor to generate a processed string which is (close to) uniform and private from Eve with the confidence specified at the beginning of the protocol. As Alice has kept her seed private throughout and the randomness extractor used is a strong one, she can then simply append her entire seed to the output of the randomness extractor to produce a final expanded string, which is guaranteed to be longer than the seed so long as a super-classical CHSH game has occurred.