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The interest in a system often resides in the interplay among differentparameters governing its evolution. It is thus often required to access many ofthem at once for a complete description. Assessing how quantum enhancement insuch multiparameter estimation can be achieved depends on understanding themany subtleties that come into play: establishing solid foundations is key todelivering future technology for this task. In this article we discuss thestate of the art of quantum multiparameter estimation, with a particularemphasis on its theoretical tools, on application to imaging problems, and onthe possible avenues towards the next developments.

A perspective on multiparameter quantum metrology: from theoretical tools to applications in quantum imaging