Algebraic and decision-theoretic ways into quantum resource theories

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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.