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Algebraic and decision-theoretic ways into quantum resource theories

量子资源理论的代数和决策理论方法

基本信息

批准号：
20K03746
负责人：
Buscemi F.
金额：
$ 2.75万
依托单位：
Nagoya University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2020
资助国家：
日本
起止时间：
2020-04-01 至 2024-03-31
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-20K03746/
关键词：
thermodynamic resources information engine quantum error-correction quantum guesswork communication channels fluctuation relations quantum entanglement quantum thermodynamics quantum channels quantum information resource theories sta

项目摘要

During FY2022 many projects that had to be postponed due to the COVID pandemics have resumed and have resulted in various important works, directly related to this project. The research achievements in FY2022 comprise two published papers, 5 arXiv preprints, and 9 invited talks. In what follows I will report about papers that have been already published.In the paper "Thermodynamic Constraints on Quantum Information Gain and Error Correction: A Triple Trade-Off" we explored the relationship between quantum error correction and quantum thermodynamics, and derived an upper bound on the measurement heat dissipated during the error-identification stage in terms of the Groenewold information gain. We also showed that under a set of physically motivated assumptions, this leads to a fundamental triple trade-off relation, which implies a trade-off between the maximum achievable fidelity of error-correction and the super-Carnot efficiency that heat engines with feedback controllers have been known to possess.In the paper "Von Neumann's information engine without the spectral theorem" we explored the role of the spectral theorem in von Neumann's argument for obtaining the formula for the entropy of a quantum state. We showed that the role of the spectral theorem can be taken over by the operational assumptions of repeatability and reversibility. As a byproduct, we obtained the Groenewold information gain as a natural monotone for a suitable ordering of instruments, providing it with an operational interpretation valid in quantum theory and beyond.

在2022财年，许多因COVID大流行而不得不推迟的项目已经恢复，并导致了与该项目直接相关的各种重要工作。FY2022年度的研究成果包括发表论文2篇，预印本5篇，特邀演讲9篇。在接下来的文章中，我将报告已经发表的论文。在“量子信息增益和误差校正的热力学约束：三重权衡”一文中，我们探讨了量子误差校正与量子热力学之间的关系，并推导了误差识别阶段测量散热的上界，即格林沃尔德信息增益。我们还表明，在一组物理动机的假设下，这导致了一个基本的三重权衡关系，这意味着误差校正的最大可实现保真度和已知具有反馈控制器的热机的超级卡诺效率之间的权衡。在“没有谱定理的冯·诺依曼信息引擎”一文中，我们探讨了谱定理在冯·诺依曼获得量子态熵公式的论证中的作用。我们证明了谱定理的作用可以被可重复性和可逆性的操作假设所取代。作为一个副产品，我们获得了格林沃尔德信息增益作为一个自然单调的适当排序的仪器，提供了一个有效的量子理论和超越的操作解释。