Uncertainty Principle, Conservation Laws, and Quantum Computing

不確定性原理･保存法則･量子計算 [in Japanese] Uncertainty Principle, Conservation Laws, and Quantum Computing [in Japanese]

- 小澤正直 OZAWA Masanao
- 東北大学大学院情報科学研究科

References (38)
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Author(s)

- 小澤正直 OZAWA Masanao
- 東北大学大学院情報科学研究科

Abstract

古典力学は,過去の状態を完全に知れば,それ以後の物理量の値を完全に知りうるという決定論的世界観を導いたが,量子力学は,測定行為自体が対象を乱してしまい,対象の状態を完全に知ることはできないことを示した.ハイゼンベルクは,不確定性原理により,このことを端的にかつ数量的に示すことに成功したといわれてきたが,測定がどのように対象を乱すのかという点について,これまでの関係式は十分に一般的ではなかった.最近の研究により,この難点を解消した新しい関係式が発見され,これまで個別に得られてきた量子測定の精度や量子情報処理の効率の量子限界を統一的に導く第一原理の役割を果たすことが明らかになってきた.

Classical mechanics leads to the deterministic view on the world, according to which the complete knowledge on the past state derives the complete knowledge on future values of physical quantities, whereas quantum mechanics shows that it is impossible to know the past state completely since measurements disturb the state of the measured object. It has long been said that Heisenberg succeeded in expressing this as a simple quantitative relation by his uncertainty principle. However, the relation was not general enough in expressing the quantitative relation between the measurement noise and disturbance. Recently, a new relation was found to solve this problem, and it has become clear that the new relation plays a role of the first principle to derive various quantum limits, some of which are obtained individually, on quantum measurements and quantum information processing in a unified treatment. This paper surveys the above development on the new formulation of uncertainty principle and its applications to quantum computing.

Journal

日本物理學會誌

日本物理學會誌 59(3), 157-165, 2004-03-05

The Physical Society of Japan (JPS)

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不確定性原理･保存法則･量子計算 [in Japanese] Uncertainty Principle, Conservation Laws, and Quantum Computing [in Japanese]

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References: 38

Cited by: 1

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