Assume that Φ : 𝕄n(ℂ)→𝕄n(ℂ) is a superoperator which preserves hermiticity. We give an algorithm determining whether Φ preserves semipositivity (we call Φ positive in this case). Our approach to the problem has a model-theoretic nature, namely, we apply techniques of quantifier elimination theory for real numbers. An approach based on these techniques seems to be the only one that allows to decide whether an arbitrary hermiticity-preserving Φ is positive. Before we go to detailed analysis of the problem, we argue that quantifier elimination for real numbers (and also for complex numbers) can play a significant role in quantum information theory and other areas as well.

中文翻译：

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在保留实数半正性和量词消除理论的地图上

假使，假设Φ ： 𝕄n(ℂ)→𝕄n(ℂ)是一个保持封闭性的超级算子。我们给出一个算法来判断是否Φ保留半正性（我们称Φ 积极的在这种情况下）。我们解决问题的方法具有模型理论性质，即我们将量词消除理论技术应用于实数。一种基于这些技术的方法似乎是唯一一种可以决定是否任意保持隐蔽性的方法Φ是积极的。在我们对问题进行详细分析之前，我们认为实数（以及复数）的量词消除在量子信息论和其他领域也可以发挥重要作用。