Understanding boundary effects in quantum state tomography – One qubit case
- Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan)
- Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Institute for Nano Quantum Information Electronics, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505 (Japan)
For classical and quantum estimation with finite data sets, the estimation error can deviate significantly from its asymptotic (large data set) behavior. In quantum state tomography, a major reason for this is the existence of a boundary in the parameter space imposed by constraints, such as the positive semidefiniteness of density matrices. Intuitively, we should be able to reduce the estimation error by using our knowledge of these constraints. This intuition is correct for maximumlikelihood estimators, but the size of the reduction has not been evaluated quantitatively. In this proceeding, we evaluate the improvement in one qubit state tomography by using mathematical tools in classical statistical estimation theory. In particular, we show that the effect of the reduction decreases exponentially with respect to the number of data sets when the true state is mixed, and it remains at arbitrarily large data set when the true state is pure.
- OSTI ID:
- 22390727
- Journal Information:
- AIP Conference Proceedings, Vol. 1633, Issue 1; Conference: 11. International Conference on Quantum Communication, Measurement and Computation, Vienna (Austria), 30 Jul - 3 Aug 2012; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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