# DIQKD is here!

This has been a momentous week for quantum information science. The long-awaited for experimental demonstration of device-independent quantum key distribution (DIQKD) is finally here! And not one only demonstration, but three in a row. First, the Oxford experiment came out, which motivated the München and the Hefei experiments to get their data out quickly to make it clear they did it independently.

To give a bit of context, for decades the community had been trying to do a loophole-free violation of a Bell inequality. To the perennial criticism that such an experiment was pointless, because there was no plausible physical model that exploited the loopholes in order to fake a violation, people often answered that a loophole-free Bell test was technologically relevant, as it was a pre-requisite for DIQKD.1 That was finally achieved in 2015, but DIQKD had to wait until now. It’s way harder, you need less noise, higher detection efficiency, and much more data in order to generate a secure key.

Without further ado, let’s look at the experimental results, summarized in the following table. $\omega$ is the probability with which they win the CHSH game, distance is the distance between Alice and Bob’s stations, and key rate is the key rate they achieved.

Experiment $\omega$ Distance Key rate
Oxford 0.835 2 m 3.4 bits/s
München 0.822 700 m 0.0008 bits/s
Hefei 0.756 220 m 2.6 bits/s

I’ve highlight the München and the Hefei key rates in red because they didn’t actually generate secret keys, but rather estimated that this is the rate they would achieve in the asymptotic limit of infinitely many rounds. This is not really a problem for the Hefei experiment, as they were performing millions of rounds per second, and could thus easily generate a key. I suspect they simply hadn’t done the key extraction yet, and rushed to get the paper out. For the München experiment, though, it is a real problem. They were doing roughly 44 rounds per hour. At this rate it would take years to gather enough data to generate a key.

Why is there such a drastic difference between Hefei and München? It boils down to the experimental technique they used to get high enough detection efficiency. Hefei used the latest technology in photon detectors, superconducting nanowire single-photon detectors,2 which allowed them to reach 87% efficiency. München, on the other hand, used a completely different technique: they did the measurement on trapped atoms, which has efficiency of essentially 100%. The difficulty is to entangle the atoms. To do that you make the atoms emit photons, and do an entangled measurement on the photons, which in turns entangles the atoms via entanglement swapping. This succeeds with very small probability, and is what makes the rate so low.

What about Oxford? Their experimental setup is essentially the same as München, so how did they get the rate orders of magnitude higher? Just look at the distance: in Oxford Alice and Bob were 2 metres apart, and in München 700 metres. The photon loss grows exponentially with distance, so this explains the difference very well. That’s cheating, though. If we are two metres apart we don’t need crypto, we just talk.

One can see this decay with distance very well in the Hefei paper: they did three experiments, with a separation of 20, 80, and 220 metres, and key rates of 466, 107, and 2.6 bits/s. In the table I only put the data for 220 metres separation because that’s the only relevant one.

It seems that the Hefei experiment is the clear winner then, as the only experiment achieving workable keyrates over workable distances. I won’t crown them just yet, though, because they haven’t done a standard DIQKD protocol, but added something called “random post-selection”, which should be explained in a forthcoming paper and in the forthcoming Supplemental Material. Yeah, when it appears I’ll be satisfied, but not before.

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### 2 Responses to DIQKD is here!

1. Daniel Harvey says:

But the Hefei experiment it all on the same table, how does it help with loop holes?

2. Mateus Araújo says:

The locality loophole is not relevant for DIQKD, we need to assume anyway that the laboratories are shielded, so we don’t gain anything by doing Alice and Bob’s measurements with space-like separation. It is relevant for Alice and Bob to be distance so that doing crypto is not pointless. Now the Hefei experiment simulated this distance by having a lot of optical fibre spooled inside their laboratory. It doesn’t matter, the photon loss is the same if 220 metres of fibre are spooled or going straight, it does show that you can generate the key at a distance.

The München experiment made an effort to physically put Alice and Bob far away, which I find cute but not really relevant. Note that the geodesic distance between their labs is 400 metres; the 700 metres that I quoted is the distance along the fibre, and I think the latter is what matters.