Quantum Detection Problem via Fusion Frames

The quantum detection problem was considered recently for discrete frames in both finite and infinite dimensional Hilbert spaces and also for continuous frames. The quantum detection problem ask to characterize the POVM ( positive operator-valued measures) that are informationally complete. It can be split as follows: the injective or state separability problem and the rang analysis or state estimation problem. Improving and extending this notion, in this note we will study the quantum detection problem for fusion frames.