In quantum theory, measurement is usually thought as a destructive operation, turning quantum superpositions into classical outcomes. However, it can also be used to drive non-trivial quantum dynamics as exemplified by measurement-based quantum computation as well as ancilla-driven quantum computation. The back-action onto a system due to its measurement can lead to various types of evolution, from complete projection to a single state, to coherent unitary rotations, as well as intermediate outcomes.
Recent results include the ability to generate holonomic quantum gates using degenerate projections, and showing methods of reversing measurement (“unlearning quantum information“) as well as demonstrating its bounds. More generally, we are interested in characterizing the ability of various system-probe interactions to perform different functions, from extracting information to implementing general completely-positive quantum maps.