| 研究実績の概要 |
As promised in the submitted project plan, I started tackling from various angles the problem of characterizing quantum temporal correlations, that is, the set of input-output correlations that can be established utilizing a given quantum channel.
The first result (published in Physical Review Letters, vol. 118) solves the problem in full generality when the quantum channel is actually a one-qubit measurement. This constitutes the simplest scenario, but it has great practical relevance, as it comprises the basic building-blocks of any, present or future, quantum computing device. Moreover, the solution we provide is given as a closed analytical formula, which can hence be efficiently used in numerical simulations and analysis of data coming from real experiments. This result paves the way to engineer new tests to benchmark quantum devices (see below "Future Work" for more details).
The second result (published in Physical Review Letters, vol. 119) instead explores the structure of quantum temporal correlations from a more fundamental viewpoint. Here we propose to complement Einstein's "no-signaling" principle with a new one, called "no-hypersignaling," which prevents too-good-to-be-true communications in physical scenarios. Such scenarios would occur, for example, if by sending N physical bits, more than N informational bits could be communicated. Surprisingly, it turns out that the proof that quantum theory indeed does not allow hypersignaling is a highly non-trivial theorem. We also show that it is possible to construct hypersignaling toy-model theories.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
1: 当初の計画以上に進展している
理由
The original goal of this project was to study quantum temporal correlations using the theory of statistical comparison (Blackwell's theorem) and to apply such insights in emerging areas such as quantum thermodynamics. While both these ideas have been explored and presented already in conferences and in pre-prints currently under evaluation (with high chances of acceptance), important side-projects have emerged in the meanwhile. Such side-projects already produced two papers published in Physical Review Letters.
This means that the problem of quantum temporal correlations is far deeper and vaster than initially thought, and that more directions of investigation are in fact possible. In particular, while the original plan was mostly mathematical in nature, we now have unexpected results that can be used to analyze data coming from practical experiments and inform the preparation of new ones. We expect that such new results (still to be announced) may turn out to provide useful tools able to benchmark quantum computing platforms.
In conclusion, while the promises made in the initial proposal have all been fulfilled, new unexpected research directions, with high potential impact for the fields of quantum information and statistics, have been found.
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| 今後の研究の推進方策 |
During the second year, the main target is to finalize the two original goals, that is, the characterization of quantum temporal correlations from the viewpoint of quantum statistical decision problems and the quantum Blackwell theorem, and its application to quantum thermodynamics. In fact, my collaborators and I have already tackled such question, but both paper are still unpublished at the moment of reporting. These achievements will hence be postponed to the final report to be provided next year.
Hence, simultaneous efforts can be directed towards exploring the new unexpected directions of research and conceiving practical tests to benchmark quantum channels and quantum measurements. In fact, the new tools we are working on at the moment may be intimately connected with quantum statistical decision problems and quantum thermodynamics. More precisely, in order to progress in this direction, we need to formulate precise statements to describe quantitative inferences in the presence of partial information. Such statements seem to have some implications also in quantum statistical mechanics and, hence, quantum thermodynamics.
As a consequence, our plans for future research are divided in three parts: (1) to go back and fulfill the initial goals of the project; (2) to explore possible applications of the analytical characterization formula for quantum channels and measurement; finally, (3), to try to formulate a general framework able to describe in a unified fashion both points (1) and (2) above.
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