Information scan of quantum states based on entropy-power uncertainty relations

We use Renyi-entropy-power-based uncertainty relations to show how the information probability distribution associated with a quantum state can be reconstructed in a process that is analogous to quantum-state tomography. We illustrate our point with the so-called "cat states", which are of both fundamental interest and practical use in schemes such as quantum metrology, but are not well described by standard variance-based approaches.