Please use this identifier to cite or link to this item: https://doi.org/10.1088/1367-2630/14/8/085007
Title: Minimax mean estimator for the trine
Authors: Ng, H.K.
Phuah, K.T.B.
Englert, B.-G. 
Issue Date: Aug-2012
Source: Ng, H.K., Phuah, K.T.B., Englert, B.-G. (2012-08). Minimax mean estimator for the trine. New Journal of Physics 14 : -. ScholarBank@NUS Repository. https://doi.org/10.1088/1367-2630/14/8/085007
Abstract: We explore the question of state estimation for a qubit restricted to the x-z-plane of the Bloch sphere, with the trine measurement. In our earlier work (H K Ng and B-G Englert 2012 Int. J. Quantum Inf. 11 1250038), similarities between quantum tomography and the tomography of a classical die motivated us to apply a simple modification of the classical estimator for use in the quantum problem. This worked very well. In this article, we adapt a different aspect of the classical estimator to the quantum problem. In particular, we investigate the mean estimator, where the mean is taken with a weight function identical to that in the classical estimator but now with quantum constraints imposed. Among such mean estimators, we choose an optimal one with the smallest worst-case error-the minimax mean estimator-and compare its performance with that of other estimators. Despite the natural generalization of the classical approach, this minimax mean estimator does not work as well as one might expect from the analogous performance in the classical problem. While it outperforms the often-used maximum-likelihood estimator in having a smaller worst-case error, the advantage is not significant enough to justify the more complicated procedure required to construct it. The much simpler adapted estimator introduced in our earlier work is still more effective. Our previous work emphasized the similarities between classical and quantum state estimation; in contrast, this paper highlights how intuition gained from classical problems can sometimes fail in the quantum arena. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
Source Title: New Journal of Physics
URI: http://scholarbank.nus.edu.sg/handle/10635/97220
ISSN: 13672630
DOI: 10.1088/1367-2630/14/8/085007
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