Assume that $\mathrm{\Phi }:{𝕄}_n(ℂ)\to {𝕄}_n(ℂ)$ is a superoperator which preserves hermiticity. We give an algorithm determining whether $\mathrm{\Phi }$ preserves semipositivity (we call $\mathrm{\Phi }$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 $\mathrm{\Phi }$ 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.

假使，假设 $\mathrm{\Phi }：{𝕄}_{ñ}（ℂ）\to {𝕄}_{ñ}（ℂ）$是保留遗传性的超级运算符。我们给出一种算法来确定是否$\mathrm{\Phi }$ 保持半正性（我们称之为 $\mathrm{\Phi }$在这种情况下为正）。我们对问题的处理具有模型理论的性质，即，我们对实数应用量词消除理论。基于这些技术的方法似乎是唯一可以确定是否保留任意遗传率的方法。$\mathrm{\Phi }$是积极的。在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理论和其他领域中也可以发挥重要作用。