2017 Fiscal Year Annual Research Report
Entanglement and nonlocality in quantum theory
| Project/Area Number |
16F16769
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| Research Institution | The University of Tokyo |
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Principal Investigator |
村尾 美緒 東京大学, 大学院理学系研究科(理学部), 教授 (30322671)
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| Co-Investigator(Kenkyū-buntansha) |
COELHO QUINTINO MARCO TULIO 東京大学, 理学(系)研究科(研究院), 外国人特別研究員
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| Project Period (FY) |
2016-11-07 – 2019-03-31
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| Keywords | 量子非局所性 / エンタングルメント / 高階量子演算 |
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| Outline of Annual Research Achievements |
In this year we have made considerable progress on the research in the topic of higher-order operations that we have started in Murao’s group last year. We have found a universal quantum algorithm that is able to transform multiple uses of a general unitary quantum operation into its inverse. This quantum algorithm allows the inversion of an arbitrary (whose description may not be known) reversible quantum operation and has potential for applications in different areas of quantum computation and quantum information processing.
This research for a quantum algorithm to invert a general unitary operation also guided us to some other related fundamental questions on quantum mechanics. In particular, which quantum operations can be realized when more than a single copy of the input-state is accessible. If a single copy of an arbitrary state is available, such operations are well understood and correspond mathematically to quantum channels, completely positive linear maps. But if one has access to more copies of the input-state, one can “consume” these copies as a resource to implement other class of operations such as non-completely positive maps.
We have then started a project to characterize and to understand what can be done in physical scenarios where one has access to many copies of a quantum state, problem that we showed to be deeply related to obtaining a universal quantum algorithm to invert general unitary quantum operations.
Also, the paper “Most incompatible measurements for robust steering tests” was accepted for publication in Physical Review A.
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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
We have constructed probabilistic universal algorithms to transform multiple uses of a general unitary operation into its inverse, whose probability of success increases when more uses are accessible. Currently, we are analyzing our algorithms to check weather the success probability can be improved, what are the required resources to improve this success probability, and looking for a systematic method to construct such algorithms.
For the project related to quantum transformations with multiple copies of input-state, we have proven a characterization theorem that allows us to understand how many copies are required to physically implement an operation that is not completely positive. Currently, we are investigating the implications of this result and looking for practical implementations.
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| Strategy for Future Research Activity |
For the next year we are going to look for applications of the quantum algorithms and results we have obtained this year. For that, we are going to analyze various topics and standard problems in quantum computation and quantum information processing, and to check weather our results and methods can be applied. We are also going to analyze the role of causal order in the unitary inversion problem. Coherent superposition of a quantum process may not lead to an algorithm with a definite causal order and may outperform causally ordered algorithms.
Also, with the results we obtained this year, we are going to write two papers, one on universal algorithms for inverting quantum operations and one on quantum transformations involving multiple copies of the input-state.
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