It would be hard to definitively prove one performance benefit over the other scientifically.
Your hypothesis is that pair programming increases developer performance and improves quality. Your test will involve giving a pair a set of requirements constrained to a specific architecturen and having them implement it.
Your control in this case is that you give the same requirements to a single developer of equal standing, skill and experience (as judged objectively by his peers) and also constrained within the same architecture.
To verify your hypothesis of time performance, the pair programmers must complete their work in less than half the time as the control. To verify your hypothesis on quality you must have the experiment pair and the control code reviewed by an objective third party, and have an objective QA group test the results of both groups without telling them which team produced what. The pair programming group must have better code and less bugs.
It is not a perfect experiment but I would be fascinated to hear if anybody has attempted something similar.
Besides this however I can't see how you can factually prove that Pair Programming is superior to a single programmer on a given feature.