论文标题
估计设计结构的povms的香农熵和（联合国）确定性关系
Estimating the Shannon entropy and (un)certainty relations for design-structured POVMs
论文作者
论文摘要
概率分布的各种特征之间的互补关系是信息理论的核心。特别是，熵功能的下限和上限非常重要。在应用主题中，我们经常处理某些概率能力的总和。主要问题是如何将施加的限制转换为香农熵的双向估计。它以两种不同的方式解决。它们越直观的是基于泰勒类型的截断膨胀。另一种方法是基于移动Chebyshev多项式的系数的使用。我们在这里提出了一个多项式系列，用于从下面估算香农熵。结果，从某种意义上说，估计值在特定点不会变得太大。提出的方法用于得出分配给量子设计的积极操作员值措施的不确定性和确定性关系。由于潜在的量子信息科学使用，量子设计目前是主动研究的主题。结果表明，派生的估计值适用于量子断层扫描和检测量子状态的可持续性。
Complementarity relations between various characterizations of a probability distribution are at the core of information theory. In particular, lower and upper bounds for the entropic function are of great importance. In applied topics, we often deal with situations, where the sums of certain powers of probabilities are known. The main question is how to convert the imposed restrictions into two-sided estimates on the Shannon entropy. It is addressed in two different ways. The more intuitive of them is based on truncated expansions of the Taylor type. Another method is based on the use of coefficients of the shifted Chebyshev polynomials. We propose here a family of polynomials for estimating the Shannon entropy from below. As a result, estimates are more uniform in the sense that errors do not become too large in particular points. The presented method is used for deriving uncertainty and certainty relations for positive operator-valued measures assigned to a quantum design. Quantum designs are currently the subject of active researches due to potential use in quantum information science. It is shown that the derived estimates are applicable in quantum tomography and detecting steerability of quantum states.
