Developing the theory of measurement reproduction

In a recent paper, Linden and Skrzypczyk outline a protocol for using imperfect measurements to reproduce perfect measurements. By splitting quantum information across multiple registers,
measurement errors can be shown to have an exponentially decreasing effect on the output distribution. This simple idea opens up theoretical and practical avenues of questioning in quantum information theory, sensing, and computation. The project will involve work in three directions. The protocol will be extended to multiple input states, with possible relations to block coding in classical information theory. It may also be possible to look at asymptotic behaviour to characterise the rate at which quantum information can be inferred from a given imperfect measurement. Also, an amendment using a feed-forward approach will be considered, where past measurement outcomes can inform what future measurements are made to maximise information gain. Additionally, the protocol will be considered for use in error mitigation. The three directions will be initially considered as independent subprojects, although there may be links to be found between them.