A new approach to Quantum Estimation: Theory and Applications

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A new approach to Quantum Estimation Theory will be introduced, based on the novel notions of \'quantum comb\' and \'quantum tester\', which generalize the customary notions of \'channel\' and \'POVM\' [PRL 101 060401 (2008)]. The new approach opens completely new possibilities of optimization in Quantum Estimation, beyond the classic approach of Helstrom and Holevo. Using comb theory it is possible to optimize the input-output arrangement of the black boxes for estimation with many uses. In this way it is possible to prove equivalence of arrangements for optimal estimation of unitaries, and the need of memory assisted protocols for for optimal discrimination of memory channels [arXive:0806.1172]. This also leads to a new notion of distance for channels with memory. Using the theory of quantum testers the optimal tomography schemes are derived---both state and for channel tomography---for arbitrary prior ensemble and arbitrary representation [arXive:0803.3237]. Finally, using the method of generalized pseudo-inverse for optimal data-processing [PRL. 98 020403 (2007)], we derived two improved data-processing for quantum tomography: Adaptive Bayesian and Frequentist [arXive:0807.5058].