# Major Security proofs available for Device-Independent QKD

I've lately started working on a DI-QKD project. I've started looking into Vazirani and Vidick's PRL paper on Device-Independent QKD security proof. It's proving to be quite time-consuming for me to go through all of the proofs.
I'm curious if there are any other well-known security proofs for DI-QKD that go in a different way from Vazirani and Vidick's. So that I can get a general estimate of how many more proofs I'll need to read in order to cover all of DI-security QKD's proofs. In order for me to be able to allocate my time properly.
Or is this the main paper, and only minor changes have been made to it since then?

If you have any familiarity with DI-QKD, it would be helpful if you could give me some insight or point me to some of the important security proofs available. Alternatively, find an article or review paper that addresses these DI-QKD-related subjects.
It would also be beneficial for future students who would like to understand DI-QKD.

• If you have the opportunity to buy something, I can recommend this recent book by Federico Grasselli, specifically the last chapter.
– JSdJ
Oct 1, 2021 at 7:21
• Also, check reference $31-39$ of 2004.14263.
– JSdJ
Oct 1, 2021 at 7:27

Roughly the idea is that the security proof definitions require us to bound the total smooth min-entropy $$H_{\min}^{\epsilon}(A_1\dots A_n|X_1 \dots X_n E)$$ of the $$n$$ round protocol and the entropy accumulation theorem tells us that we can bound this as $$H_{\min}^{\epsilon}(A_1\dots A_n|X_1 \dots X_n E) > n t - O(\sqrt{n})$$ where $$t$$ is a lower bound on $$H(A|XE)$$, i.e., the conditional von Neumann entropy accrued in a single round. Thus the entropy accumulation does a lot of the hard work by bounding the $$n$$-round quantity by a 1-round quantity and allowing us to focus of bounding this simpler quantity (although still not necessarily that simple and a lot of work focuses now on computing this quantity).