2016 Fiscal Year Annual Research Report
量子論における同時操作不可能性とその順序構造による特徴づけ
| Project/Area Number |
16F16702
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| Research Institution | Kyoto University |
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Principal Investigator |
宮寺 隆之 京都大学, 工学研究科, 准教授 (50339123)
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| Co-Investigator(Kenkyū-buntansha) |
HAAPASALO ERKKA 京都大学, 工学研究科, 外国人特別研究員
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| Project Period (FY) |
2016-07-27 – 2018-03-31
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| Keywords | Quantum Theory / Quantum Measurement |
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| Outline of Annual Research Achievements |
For the past year I have concentrated on joint and sequential measurements and optimality properties of quantum measurements. With T. Heinosaari and Y. Kuramochi, we have investigated non-demolition measurements and strings of repetitions of such measurements. We particularly concentrated on noise-cancellation in such scenarios. We have shown that repeated measurement can be used to extract the meaningfull information of a fuzzy observable; see list of publications. With T. Miyadera and T. Heinosaari, we have studied least disturbing quantum measurements; measurements that allow as much further minimally disturbed operations afterwards. We have particularly concentrated on different optimality criteria for measurement realizations for an observable, i.e., properties of the quantum channel associated to the measurement. We have obtained mathematical and operational characterizations for the class of such least disturbing measurements and channels which will be published soon. With J.-P. Pellonpaa, I have investigated different optimality criteria and their characterizations for quantum observables. We have particularly concentrated on continuous observables and the joint measurements of different optimal observables. This paper in preparation reviews several known optimality results for discrete observables and deepens them and generalizes them for continuous observables. Thus, we obtain characterizations for observables which are free from different types of classical noise and free from quantum noise.
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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
Current status is rather fine. We have succeeded in generalizing the findings obtained for the discrete observables to the continuous observables.
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| Strategy for Future Research Activity |
With J.-P. Pellonpaa we have started studying covariant quantum devices (devices that mirror the symmetries present in the physical system) as a continuation of an earlier project. We will especially concentrate on positive covariant kernels, their structure, and optimality properties. These kernels generalize the notions of quantum observables, channels, and instruments and are useful in generalizations of traditional quantum theory. As a special example, we study kernels on operator algebras which are covariant with respect to the modular automorphism group of the algebra. I have been studying multipartite incompatibility, its detection and quantification. Quantum measurement devices are compatible if they can be joined within a single measurement device. The best known case of this situation is bipartite compatibility, i.e., the case where there are two devices. However, often one has to study approximate joint devices for several often incompatible quantum measurement devices. It is immediate that the more devices one has to join (approximately) the more difficult this joining becomes. I am looking at the connections and relations between the degree of incompatibility of a larger set of incompatible devices to the degree of incompatibility of different subsets of the entire set. To quantify incompatibility, I will use different strategies: by quantifying the noise that has to be added to the devices to make them compatible and by measuring the necessary approximations to make the devices compatible using, e.g., quantum relative entropy.
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