Algebraic and decision-theoretic ways into quantum resource theories

于2022财政年度，多个因COVID大流行而须延期的项目已恢复进行，并已完成多项与该项目直接相关的重要工程。2022财年的研究成果包括两篇已发表论文、5篇arXiv预印本及9场特邀演讲。在论文“Thermodynamic Constraints on Quantum Information Gain and Error Correction：A Triple Trade-Off”中，我们探讨了量子纠错和量子热力学之间的关系，并根据Groenewold信息增益导出了错误识别阶段的测量热耗散上限。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，这意味着在误差校正的最大可达保真度和具有反馈控制器的热机所具有的超卡诺效率之间进行权衡。我们探讨了谱定理在冯·诺依曼论证量子态熵公式时的作用。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Groenewold信息增益作为一个自然的单调性的一个适当的排序的仪器，提供了一个有效的操作解释在量子理论和超越。

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.