Abstract

Localization of quantum Bernoulli noises (LQBNs) are the family of local annihilation and local creation operators acting on Bernoulli functionals. In this paper, we construct a density operator ρ_k represented by LQBNs, and define a new quantum entropy $S({\rho }_k)$ based on LQBNs. Furthermore, we demonstrate that this quantum entropy $S({\rho }_k)$ also has the basic properties of von Neumann entropy, such as concavity, subadditivity, and nonnegativity. In particular, we obtain the necessary and sufficient condition for $S({\rho }_k)=k.$

中文翻译：

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就局部量子伯努利噪声和相关性质而言的量子熵

摘要

量子伯努利噪声 (LQBN) 的局部化是作用于伯努利泛函的局部湮没和局部创建算子家族。在本文中，我们构造了一个由 LQBNs 表示的密度算子ρ _{k ，并定义了一个新的量子熵}$\mathrm{小号}({\rho }_{ķ})$基于 LQBN。此外，我们证明了这种量子熵$\mathrm{小号}({\rho }_{ķ})$还具有冯诺依曼熵的基本性质，如凹性、次可加性和非负性。特别是，我们得到了$\mathrm{小号}({\rho }_{ķ})=ķ.$