| 研究概要 |
1. We addressed the problem how to provide efficient protocols for communication over quantum channels. The maximal amount of classical information conveyed for fixed encoding (resp., decoding) is commonly referred to as accessible information (resp., informational power). An analytical expression for accessible information and informational power is not known in the general. case. In this year, we derived tight upper and lower bounds for these quantities in the general (discrete or continuous) case, using the ensemble-measurement duality theorem. Also, we provided refined bounds for the relevant case of so-called SIC encoding or decoding, commonly used e.g. for quantum tomography. Our results, which have already attracted the attention of several researchers in the field, are expected to play a crucial role in quantum communication theory, quantum measurement theory, quantum cryptography, and quantum error correction.
2. We addressed the problem to derive an optimal protocol to access correlation functions in quantum theory. Indeed, due to the non-commutativity of observables, the product of two or more quantum observables is not an observable itself, and thus can not be measured as such. The protocol we derived is not only operational, namely it can be expressed in terms of a fixed pre- and post-processing, but also optimal in a statistical sense. This result has direct implications in quantum thermodynamics, quantum statistics, quantum field theory, and foundation of quantum theory, and it allows to directly test uncertainty relations. Furthermore, as promised in the original research plan for my JSPS, fellowship, I provided an experimental proposal which is suitable for implementation with present quantum optical technology.
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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
We proposed an operational scheme for directly access quantum correlation functions, thus showing, perhaps surprisingly, that they are no less operational than any other expectation value. We derived tight bounds on the accessible information and the informational power of ensembles and measurement in the arbitrary case and in the symmetric, informationally complete case. Those results are more advanced than the original plan.
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