2018 Fiscal Year Final Research Report
Development of Quantum Measurement Optimization Theory based on Bayesian Statistics
| Project/Area Number |
16K13775
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Osaka University |
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Principal Investigator |
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| Research Collaborator |
SUGIYAMA Takanori
IMORI Shinpei
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Keywords | ベイズ統計 / 統計的決定理論 / 量子情報 / モンテカルロ法 / 量子計算機 / ゲートセットトモグラフィ |
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| Outline of Final Research Achievements |
The ultimate goal of our research is to propose a systematic and universal methodology to obtain the best measurement given a specific quantum estimation problem. As a first step, we reconsider the mathematical framework of quantum statistical decision theory and extend it such that we propose a better class of measurements for finite sample cases and justify it by using the approximation method (asymptotic theory). In toy example, according to our proposed methodology we find the measurement yielding smaller estimation error than traditional one. It can be easily implemented in an actual quantum experiment.
As for practical application, we have to consider numerical methods and regularizations in the current level of quantum experiments. We show the (mathematical) consistency of a class of regularized estimators in the context of self-consistent quantum tomography.
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| Free Research Field |
量子ベイズ統計
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| Academic Significance and Societal Importance of the Research Achievements |
例えば、非可換な２つのobservable (X, Y)の期待値を実験的にデータから推定することを考える。量子力学の教科書的には、X,Yの２種類の射影測定をN/2回ずつ行うことが自然であり、誰も疑わずに使っている。量子推定の既存研究は原理的な推定誤差の下限を達成する方法を与えているが、理想的な条件下の話であり技術的な難易度が高い。しかし、本研究成果を利用すれば４種類の射影測定でN/4回ずつ測定して、一様に推定誤差を減らせることがわかる。
このように、本研究の成果が適用できれば、現在の実験現場で理想的な条件でなくとも、無理せず推定誤差を減らす方法が提案できる。
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