**October 29, 2014**

Got another paper out today, here: https://arxiv.org/abs/1410.7629

It’s about making random numbers based on quantum optics. If you read my last post https://jonatanbohrbrask.dk/2014/10/13/a-self-testing-quantum-random-number-generator/ (if not, go read it ðŸ™‚ ) then you know that guaranteeing something is random isn’t as easy as it sounds. Something may seem random to you but perfectly non-random to someone else. Say I’m a magician and I practised coin flipping a lot. When I flip a coin, by giving it just the right spin I can make it land on heads or tails as I wish. To you the flip looks random, but to me the outcome is completely predictable. What we want is a guarantee that the numbers we generate are random to anyone, no matter how much extra knowledge they have of the physical systems used to generate them.

Remarkably, this is actually possible in quantum physics: it is impossible to predict the outcome of some quantum measurements even when you know all there is to know about the devices used. So if you know what your quantum system is and what measurement is being made on it, it is possible to certify randomness. This is the basis for commercial quantum random numbers generators (yes, you can actually buy such a thing, https://www.idquantique.com/random-number-generation/products/).

What is even more remarkable though is that randomness can be certified even when you know essentially nothing about what is being measured or what the system is. In quantum physics, correlations generated by some experiments can be stronger than anything classical experiments can generate, and this shows up at the level of the data. I can take two black boxes that take some inputs, e.g. they have some buttons you can press, and give some outputs, for example some lights light up when you press the buttons. After playing with them for a while I can generate some statistics about what lights light up when certain buttons are pressed. If this statistics violates a so-called Bell inequality, then we know for sure that what is going on inside those boxes must be quantum. We don’t need to look inside the boxes to know this – no classical box could generate the same statistics. What is more, there is guaranteed to be some randomness in the statistics, which we can extract.

This idea is known as device-independent randomness generation, because the guarantees on the randomness do not depend on knowing anything about what is inside the black boxes. It’s a beautiful idea, and it has been around for a while, but so far there has only been one experiment which implemented it. It generated 42 random bits over about one month. Not exactly a high rate! The reason is that it is very hard to violate a Bell inequality in practice without throwing away some of the experimental data. Real experiments have losses and imperfections – sometimes the detectors in the experiment just don’t click. In the black-box picture, you press a button but no light lights up. Many experiments have violated Bell inequalities by disregarding those experimental runs. This is fine for some purposes, but for randomness generation it is a big no-go. You cannot have any device-independent guarantees on the randomness if you do that.

Fortunately, last year new experiments with light and photodetectors were finally able to get a Bell violation without throwing away any data. This is nice because experiments with light can reach much higher rates than those 42 bits per month, which were generated by measuring on trapped ions. In our paper we analyse just how much randomness one could optimally get out of such optical experiments considering realistic imperfections and using some technical results which allow us to look not just at one Bell inequality, but at all possible Bell inequalities at once and optimise over them.

** Published paper: **https://iopscience.iop.org/article/10.1088/1367-2630/17/2/022003