01 (2010 Selected)：

New development of quantum estimation theory in quantum cybernetics

Quantum estimation theory is a branch of noncommutative statistics that addresses　the problem of finding the best estimation procedure for an unknown quantum　object by a physically feasible measuring process. The main objective of the　present research is to demonstrate several fundamental results of quantum estimation　theory by means of quantum optical experiments, putting emphasis on its usefulness　and applicability in quantum information science and technology.

We first realize an adaptive quantum estimation scheme for an unknown quantum　state. In general, the optimal estimator (measurement) depends on the true state　that is to be estimated. Such a paradoxical situation is surmounted by an adaptive　estimation scheme as follows: one begins with a certain initial guess and applies the　measurement that is optimal at that state. One then applies the maximum likelihood　method to obtain the next guess, and repeat this procedure until the estimator converges.　Since this procedure enjoys the strong consistency and asymptotic efficiency,　it is expected that the adaptive estimation scheme will supersede the conventional　estimation procedures, such as the quantum tomography, that are not at all efficient.　We carry out the first experimental demonstration of an adaptive quantum　estimation scheme that is optimal in view of quantum estimation theory.

We next demonstrate some recent developments in quantum channel estimation　theory: for example, a novel quantum effect for unitary gates which asserts that　one can obtain O(n2) information about an unknown unitary gate when n identical　copies of the gate are available. We further explore a theory of estimating perturbed　quantum channels, and devise an algorithm for finding an optimal quantum estimator　based on the convex programming.

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