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Finite Sample Analysis in Quantum Estimation
English
249 b
30-day return policy
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In this thesis, the author explains the background of problems in quantum estimation, the necessary conditions required for estimation precision benchmarks that are applicable and meaningful for evaluating data in quantum information experiments, and examples of such benchmarks. The author develops mathematical methods in quantum estimation theory, and analyzes the benchmarks in tests of Bell-type correlation and quantum tomography with those methods. Above all, a set of explicit formulae for evaluating the estimation precision in quantum tomography with finite data sets are derived, in contrast to the standard quantum estimation theory, which can only deal with infinite samples. This is the first result directly applicable to the evaluation of estimation errors in quantum tomography experiments, allowing experimentalists to guarantee estimation precision and verify quantitatively that their preparation is reliable.
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