论文标题
纠缠相对熵及其概括的新添加性特性
New additivity properties of the relative entropy of entanglement and its generalizations
论文作者
论文摘要
我们证明，当\ emph {至少两种状态中的一个}属于某些特定类时，纠缠的相对熵是加性的。我们表明，这些类别包括两分纯，最大相关，GHz，贝尔对角线，各向同性和广义迪克状态。以前，仅当\ textit {两个}状态属于同一类时，才建立添加性。此外，我们将这些结果扩展到基于$α$ - $ z $rényi相对熵的纠缠单调。值得注意的是，这个单调家族还包括纠缠的一般鲁棒性和纠缠的几何测量。此外，我们证明，基于量子相对熵的任何单调对于一般状态都不是附加的。我们还计算了双方纯，对角线，各向同性，广义Werner，广义Dicke和最大相关的钟形钟形状态的单调的封闭形式表达式。我们的结果依赖于开发一种方法，该方法使我们能够将初始凸优化问题重新生要为更简单的线性。即使我们主要关注纠缠理论，我们也希望我们的某些技术结果在研究更一般的凸优化问题方面可能很有用。
We prove that the relative entropy of entanglement is additive when \emph{at least one of the two states} belongs to some specific class. We show that these classes include bipartite pure, maximally correlated, GHZ, Bell diagonal, isotropic, and generalized Dicke states. Previously, additivity was established only if \textit{both} states belong to the same class. Moreover, we extend these results to entanglement monotones based on the $α$-$z$ Rényi relative entropy. Notably, this family of monotones includes also the generalized robustness of entanglement and the geometric measure of entanglement. In addition, we prove that any monotone based on a quantum relative entropy is not additive for general states. We also compute closed-form expressions of the monotones for bipartite pure, Bell diagonal, isotropic, generalized Werner, generalized Dicke, and maximally correlated Bell diagonal states. Our results rely on developing a method that allows us to recast the initial convex optimization problem into a simpler linear one. Even though we mostly focus on entanglement theory, we expect that some of our technical results could be useful in investigating more general convex optimization problems.
