Quantum Estimation by Local Observables

Quantum estimation theory provides optimal observations for various estimation problems for unknown parameters in the state of the system under investigation. However, the theory has been developed under the assumption that every observable is available for experimenters. Here, we generalize the theory to problems in which the experimenter can use only locally accessible observables. For such problems, we establish a Cram{\'e}r-Rao type inequality by obtaining an explicit form of the Fisher information as a reciprocal lower bound for the mean square errors of estimations by locally accessible observables. Furthermore, we explore various local quantum estimation problems for composite systems, where non-trivial combinatorics is needed for obtaining the Fisher information.