量子測定の量子情報理論的研究

可访问信息量化了可以从量子态集合中提取的经典信息的数量。类似地，信息功率量化了可以通过量子测量提取的经典信息的数量。对于这两个量，我们给出了只依赖于系统维数的上界和下界，并证明了它们的紧密性。在对称信息完全（SIC）集成和测量的情况下，我们提供了更强的边界，并证明了它们对量子位和量子位的紧密性。从我们的上界，我们注意到，也许令人惊讶的是，由任意维度的SIC集成或测量产生的统计数据，虽然对于层析目的是最佳的，但实际上从未包含超过一个比特的信息，其余的由完全随机的比特组成。另一方面，从我们的下界，我们获得了一个明确的策略，击败了所谓的“相当不错”的策略，用于在SIC集成和测量的情况下提取互信息。

The accessible information quantifies the amount of classical information that can be extracted from an ensemble of quantum states. Analogously, the informational power quantifies the amount of classical information that can be extracted by a quantum measurement.For both quantities, we provided upper and lower bounds that depend only on the dimension of the system, and we proved their tightness. In the case of symmetric informationally complete (SIC) ensembles and measurements, we provided stronger bounds and we proved their tightness for qubits and qutrits. From our upper bounds, we noticed, perhaps surprisingly, that the statistics generated by SIC ensembles or measurements in arbitrary dimension, though optimal for tomographic purposes, in fact never contains more than just one bit of information, the rest being constituted by completely random bits. On the other hand, from our lower bounds, we obtained an explicit strategy beating the so-called "pretty-good" one for the extraction of mutual information in the case of SIC ensembles and measurements.