Information theory based on general probabilistic theories and its application to the foundation of quantum mechanics

2021 Fiscal Year Final Research Report

• Project/Area Number: 17K18107
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Theory of informatics; Mathematical physics/Fundamental condensed matter physics
• Research Institution: Shibaura Institute of Technology
• Principal Investigator: Kimura Gen 芝浦工業大学, システム理工学部, 教授 (80517011)
• Project Period (FY): 2017-04-01 – 2022-03-31
• Keywords: 量子力学基礎論 / 量子情報理論 / 一般確率論 / 量子開放系理論 / ベルの定理

Outline of Final Research Achievements

We investigated the foundations of quantum theory and quantum information theory　mainly based on general probabilistic theories. We clarified the universal relationship between the geometrical structure of the state space and information storing, and provided an information-theoretic understanding of simple questions such as why only qubit systems have point symmetry (Bloch Ball). In addition, the principle of information symmetry was developed and various information quantities were characterized based on general probabilistic theories. We also discovered the universal law of relaxation times for completely positive dynamics and a new relaxed Bell's inequality by introducing a hiddeness which characterizes the extent how much we need a hidden variable. Quantum teleportation based on the vacuum entanglement was also studied where we have clarified the optimal procol with a given entanglement.

Free Research Field

量子力学基礎論，量子情報科学

Academic Significance and Societal Importance of the Research Achievements

近年量子情報科学の発展を受けて，情報理論的な量子力学の理解の可能性が高まっている．従来は道具主義的な理解しかできていなかった量子物理学に新たな光を当てることになり，より深い理解につながることが期待される．また，様々な情報処理や物理法則の間の連関性の理解が深まり，新たな応用につながることも期待できる．例えば，我々の成果により状態空間の幾何学構造から，物理系の情報蓄積量が見積もれるようになった．また，量子開放系の研究は，量子コンピュータなどの実現の最大の障壁であるデコヒーレンスの理解を深めることになった．これらの研究は，自然観の在り方を探る基礎から情報科学への応用まで幅広い意義を持っている．