(Semi-)device-independent certification of mutually unbiased bases

As quantum technologies advance, the certification of high-dimensional quantum devices becomes more and more relevant. This is essential both for verifying the outcome of quantum computations, and for guaranteeing the security of cryptographic devices. In this talk, I will focus on the certification of quantum measurement devices performing measurements in mutually unbiased bases (MUBs) in arbitrary dimension. MUBs have a myriad of applications in quantum information processing, and therefore these measurement devices constitute basic building blocks of computational and cryptographic devices. I will discuss how to give a characterisation of MUBs that is suitable for semi-device-independent (SDI) certification, that is, certification under the assumption of fixed Hilbert space dimension. Then I will present a protocol that allows for experimental SDI certification of MUBs in arbitrary dimensions (that has since been demonstrated experimentally in dimension 4). Furthermore, I will discuss a relaxed device-independent (DI) characterisation of MUBs, referred to as mutually unbiased measurements (MUMs). While MUMs are strictly more general than MUBs, they share many operational characteristics, and I will present a protocol that allows for their DI certification

Links to the papers: https://arxiv.org/abs/1803.00363,
https://arxiv.org/abs/1912.03225