Fidelity is one of the most widely used quantities in quantum information that measure the distance of quantum states through a noisy channel. In this paper, we introduce a quantum analogy of computation tree logic (CTL) called QCTL, which concerns fidelity instead of probability in probabilistic CTL, over quantum Markov chains (QMCs). Noisy channels are modelled by super-operators, which are specified by QCTL formulas; the initial quantum states are modelled by density operators, which are left parametric in the given QMC. The problem is to compute the minimumfidelity over all initial states for conservation. We achieve it by a reduction to quantifier elimination in the existential theory of the reals. The method is absolutely exact, so that QCTL formulas are proven to be decidable in exponential time. Finally, we implement the proposed method and demonstrate its effectiveness via a quantum IPv4 protocol.

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基于保真度的量子马尔可夫链模型检验的代数方法

保真度是量子信息中使用最广泛的量之一，该量度通过噪声通道的量子态距离。在本文中，我们介绍了一种称为QCTL的计算树逻辑（CTL）的量子类比，它涉及量子马尔可夫链（QMC）上的保真度而不是概率CTL中的概率。噪声通道由超级运营商建模，超级运营商由QCTL公式指定；初始量子态由密度算子建模，密度算子在给定的QMC中保持参数化。问题是要计算所有初始状态下的最小保真度以进行保护。我们通过减少实在论中的量词消除来实现这一点。该方法绝对准确，因此QCTL公式被证明可以在指数时间内确定。最后，