We address entropic uncertainty relations between time and energy or, more precisely, between measurements of an observable $G$ and the displacement $r$ of the $G$-generated evolution $e^{-ir G}$. We derive lower bounds on the entropic uncertainty in two frequently considered scenarios, which can be illustrated as two different guessing games in which the role of the guessers are fixed or not. In particular, our bound for the first game improves the previous result by Coles et al.. Our derivation uses as a subroutine a recently proposed novel algebraic method, which can in general be used to derive a wider class of entropic uncertainty principles.

中文翻译：

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熵时间-能量不确定性关系：一种代数方法

我们解决了时间和能量之间的熵不确定性关系，或者更准确地说，在可观察的 $G$ 的测量值和 $G$ 生成的演化 $e^{-ir G}$ 的位移 $r$ 之间。我们在两个经常考虑的场景中推导出熵不确定性的下限，这可以用两种不同的猜测游戏来说明，其中猜测者的角色是固定的或不固定的。特别是，我们对第一场比赛的界限改进了 Coles 等人之前的结果。我们的推导使用了最近提出的新代数方法作为子程序，该方法通常可用于推导更广泛的熵不确定性原理。