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.

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

1 Answer 1


The progress in DIQKD security proofs has been quite rapid in recent years. In particular, the approach of Vazirani and Vidick is no longer what the community uses.

The two major approaches that I know of are using the entropy accumulation theorem or quantum probability estimation. These two approaches are quite similar in spirit but the entropy accumulation theorem approach is seemingly a lot more popular with the community. I would strongly recommend the article simple and tight device-independent security proofs for a demonstration and explanation of how to apply the entropy accumulation theorem. If you are looking to prove security of a DIQKD protocol then in my opinion the entropy accumulation theorem is the simplest method to use.

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).

Your question is well timed though, just yesterday the first experimental demonstration was performed. Their protocol was based on winning the CHSH game and their security proof used the entropy accumulation theorem. You can find the paper here.

  • $\begingroup$ Thank you for the detailed explanation. $\endgroup$
    – IamKnull
    Commented Oct 1, 2021 at 8:57

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