We study the problem of tolerant testing of stabilizer states. In particular, we give the first such algorithm that accepts mixed state inputs. Formally, given a mixed state $\rho$ that either has fidelity at least $\varepsilon_1$ with some stabilizer pure state or fidelity at most $\varepsilon_2$ with all such states, where $\varepsilon_2 \leq \varepsilon_1^{O(1)}$, our algorithm distinguishes the two cases with sample complexity $\text{poly}(1/\varepsilon_1)$ and time complexity $O(n \cdot \text{poly}(1/\varepsilon_1))$.

翻译：我们研究了稳定子态的容忍性测试问题。具体而言，我们提出了首个能够接受混合态输入的此类算法。形式化地说，给定一个混合态 $\rho$，其要么与某个稳定子纯态具有至少 $\varepsilon_1$ 的保真度，要么与所有此类态的保真度至多为 $\varepsilon_2$，其中 $\varepsilon_2 \leq \varepsilon_1^{O(1)}$。我们的算法能够以 $\text{poly}(1/\varepsilon_1)$ 的样本复杂度和 $O(n \cdot \text{poly}(1/\varepsilon_1))$ 的时间复杂度区分这两种情况。