The maximum likelihood strategy to the estimation of group parameters allows to derive in a general fashion optimal measurements, optimal signal states, and their relations with other information theoretical quantities. These results provide a deep insight into the general structure underlying optimal quantum estimation strategies. The entanglement between representation spaces and multiplicity spaces of the group action appear to be the unique kind of entanglement which is really useful for the optimal estimation of group parameters.
Sealing information means making it publicly available, but with the possibility of knowing if it has been read. Commenting on [1], we will show that perfect quantum sealing is not possible for perfectly retrievable information, due to the possibility of performing a perfect measurement without disturbance, even on unknown states. The measurement is a collective one, and this makes the protocol of quantum sealing very interesting as the only example of the power of collective measurements in breaking security.
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