2023 Fiscal Year Research-status Report
Observational entropy and statistical inference: a mathematical study
| Project/Area Number |
23K03230
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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) |
2023-04-01 – 2026-03-31
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| Keywords | macroscopic entropy / observational entropy / retrodiction / coarse-graining |
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| Outline of Annual Research Achievements |
The properties of observational entropy as a functional of quantum states and POVMs have been studied with the tools of operator algebras and mathematical statistics. It has been found that observational entropy has many connections with Petz's theory of statistical sufficiency. Such connections allowed us to clarify the meaning of "coarse-graining" as a form of statistical retrodiction. This interpretation greatly simplifies the conceptual foundations of statistical mechanics. A paper about the theory of statistical retrodiction and its formulation in quantum theory has been published. Moreover, the idea of connecting statistical mechanics and retrodiction was at the basis of another paper, published on Physical Review Letters, in which we reformulate the second law of thermodynamics as an equilibrium condition in expected utility theory. Again in connection with observational entropy, two works of the resource theory of quantum measurements have been published: one about quantum measurements incompatibility, another one about quantum measurement sharpness. Finally, in exploring the process of retrodiction in quantum theory, we published a paper about the new idea of "virtual quantum broadcasting", which shows how time-like correlations can be treated within the formalism of quantum theory.
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| Current Status of Research Progress |
Current Status of Research Progress
1: Research has progressed more than it was originally planned.
Reason
The research plan is progressing exactly as anticipated, without any delay. The first paper discussing the most important mathematical properties of observational entropy has been published as expected. Moreover, there is a series of follow-up papers that are already under preparation.
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| Strategy for Future Research Activity |
In the next stage, we plan to generalize the observational entropy to priors different from the uniform distribution. We also plan to study the evolution of observational entropy in isolated systems. Finally, we plan to study the structure of macroscopic states from an algebraic viewpoint. All these projects are very important for our understanding of the foundations of statistical mechanics.
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| Causes of Carryover |
The reason is that there has been an overlap due to the effect of pandemic in retarding the plans of a previous project, so that this year I did not need to use money from this project. We plan to use this money to invite collaborators to Japan and to attend domestic and international workshops and conferences to disseminate the results obtained so far, and collect information to continue our research successfully.
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