Self-testing of quantum systems

Violations of Bell inequalities have traditionally been used to refute a local-realistic description of the world. Not surprisingly, under the assumption that the world is quantum, they can be used to certify quantum devices. What is surprising is that in some cases this characterisation turns out to be (almost) complete, i.e.~we can determine (almost) everything about the devices and this phenomenon is known as self-testing of quantum systems. Although the first self- testing results can be traced back to the works of Tsirelson published in the 80's, the topic has remained largely unknown until the seminal work of Mayers and Yao in 1998. It has received further exposure with the advent of device-independent quantum cryptography to which it is closely connected. In this talk I will give a brief introduction to the topic of self-testing and discuss some recent developments, e.g.~robust self-testing, weak self-testing, self-testing of entangled measurements, self-testing of high-dimensional systems or self-testing in prepare-and-measure scenarios.