Self-Testing Quantum Random Number Generator

The generation of random numbers is a task of paramount importance in modern science. A central problem for both classical and quantum randomness generation is to estimate the entropy of the data generated by a given device. Here we present a protocol for self-testing quantum random number generation, in which the user can monitor the entropy in real time. Based on a few general assumptions, our protocol guarantees continuous generation of high quality randomness, without the need for a detailed characterization of the devices. Using a fully optical setup, we implement our protocol and illustrate its self-testing capacity. Our work thus provides a practical approach to quantum randomness generation in a scenario of trusted but error-prone devices.

Figure 1

Sketch of the protocol. The self-testing QRNG protocol consists of three distinct steps. (1) First, an experiment is performed where, in each round, the user chooses a preparation $x$ and a measurement $y$, and obtains an outcome $b$. (2) From the raw data, the distribution $p(b|x,y)$ can be estimated leading to an estimate for the value of the witness $W$, from which the entropy of the raw data can be quantified. (3) Based on the entropy bound, appropriate postprocessing of the raw data is performed, in order to extract the final random bit string.

Figure 2

Implementing the self-testing QRNG. (a) Experimental setup. (b) Real-time evolution of the witness value $W$ (blue) and randomness generation rate (bits extracted per second; red). After 3 h, the air conditioning in the laboratory is switched off, which leads to misalignment of the optical components. In turn, this leads to a significant drop of the witness value $W$ and corresponding entropy.