2022 Fiscal Year Research-status Report
Algebraic and decision-theoretic ways into quantum resource theories
| Project/Area Number |
20K03746
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| Research Institution | Nagoya University |
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Principal Investigator |
Buscemi F. 名古屋大学, 情報学研究科, 教授 (80570548)
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| Project Period (FY) |
2020-04-01 – 2024-03-31
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| Keywords | thermodynamic resources / information engine / quantum error-correction |
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| Outline of Annual Research Achievements |
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.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
Since the lifting of travel restrictions due to COVID, the research plan about quantum resource theories has resumed and some projects that were left to wait have been either completed or resumed at full speed. At the moment, I am working to collect the results obtained during FY 2022 into papers, presentations, and lectures for students.
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| Strategy for Future Research Activity |
The plan for FY 2023 is to summarize the projects finalized in FY 2022 into papers, research presentations, and lecture notes.
We will explore resource theories of quantum measurements. In particular, we will study the concept of "quantum incompatibility" and "measurement sharpness" from the point of view of general resource theories. Our aim is to solve some problems that have remained open in the literature. The first problem is due to the existence of two competing and inequivalent definitions for quantum incompatibility. Another problem is the lack of a clear understanding of the set of operations that do not increase the sharpness of a measurement.
We will also extend to non-commutative setting our work on the probabilstic and statistical foundations of thermodynamics and fluctuation theorems. This final part will complete some of the ideas that we put forth during the last fiscal year.
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| Causes of Carryover |
The reason for the incurring amount is that, due to the spread of COVID 19, many trips were postponed or canceled, many collaborators could not be invited, and some publications were thus delayed.
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