2023 Fiscal Year Final Research Report
A refinement of quantum information theory by algorithmic randomness
| Project/Area Number |
18K03405
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 12030:Basic mathematics-related
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| Research Institution | Chubu University |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2024-03-31
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| Keywords | 典型性原理 / 量子情報理論 / アルゴリズム的ランダムネス / 量子力学 / 多世界解釈 / 確率解釈 / ベルの不等式 / アルゴリズム的情報理論 |
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| Outline of Final Research Achievements |
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure theory, and therefore any operational characterization of the notion of probability is still missing in quantum mechanics. In our former works, based on the toolkit of algorithmic randomness, we presented an operational refinement of the Born rule, called the principle of typicality, for specifying the property of the results of quantum measurements in an operational way. We did this from the point of view of the many-worlds interpretation of quantum mechanics. In this research, we made applications of our framework to quantum information theory, including quantum error-correction and the security proof of the BB84 quantum key distribution protocol, in order to demonstrate how properly our framework works in practical problems in quantum mechanics.
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| Free Research Field |
アルゴリズム的ランダムネス
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| Academic Significance and Societal Importance of the Research Achievements |
量子力学の中核にあるボルン則（波動関数の確率解釈）とアルゴリズム的ランダムネスを直接結び付ける試みは、これまでほとんど全く存在しなかった。特に、量子力学の公理系としての形式に深く立ち入り、量子力学とアルゴリズム的ランダムネスとを結び付ける研究は、私の知る限り、本研究が世界的に初めてのものである。本研究はアルゴリズム的ランダムネスに基づいて量子力学の物理理論としての完全化を達成しようとするものであり、量子力学に対する人類の理解を格段に深めるものであると私は考える。本研究の基礎科学に対する貢献、そして本研究の人類の世界認識・宇宙認識に対する貢献は計り知れないものであると私は考える。
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