Detection of quantum information masking via machine learning

TL;DR

The paper tackles detecting quantum information masking (QIM) in quantum states using supervised learning. It shows that XGBoost can accurately classify QIM for pure qubit states, and introduces AL-XGBoost with a hybrid uncertainty-diversity strategy to effectively label informative samples for mixed states. The results demonstrate high accuracy and AUC for pure states and superior performance of AL-XGBoost over baselines, with a four-class extension illustrating potential scalability. This approach provides a practical, data-driven tool for QIM certification with implications for quantum information security and state verification.

Abstract

Recently, machine learning has been widely applied in the field of quantum information, notably in tasks such as entanglement detection, steering characterization, and nonlocality verification. However, few studies have focused on utilizing machine learning to detect quantum information masking. In this work, we investigate supervised machine learning for detecting quantum information masking in both pure and mixed qubit states. For pure qubit states, we randomly generate the corresponding density matrices and train an XGBoost model to detect quantum information masking. For mixed qubit states, we improve the XGBoost method by optimizing the selection of training samples. The experimental results demonstrate that our approach achieves higher classification accuracy. Furthermore, we analyze the area under the curve (AUC) of the receiver operating characteristic curve for this method, which further confirms its classification performance.

Figures (10)

• Figure 1: Different maskable sets on the Bloch sphere. $T _{1}$, $T _{2}$, $T _{3}$, and $T _{4}$ correspond to the maskable sets $\mathcal{C}_{0}^{0}\left(\left|\left(\frac{\pi }{3} , \frac{\pi }{4} \right)\right\rangle\right)$, $\mathcal{C}_{\frac{\pi }{4}}^{\frac{\pi }{4}}\left(\left|\left(\frac{\pi }{3} , \frac{\pi }{4} \right)\right\rangle\right)$, $\mathcal{C}_{0}^{\frac{\pi }{2}}\left(\left|\left(\frac{\pi }{3} , \frac{\pi }{4} \right)\right\rangle\right)$, and $\mathcal{C}_{\frac{\pi }{3}}^{\frac{\pi }{3}}\left(\left|\left(\frac{2\pi }{3} , \frac{\pi }{5} \right)\right\rangle\right)$ respectively.
• Figure 2: The classification accuracy of the XGBoost algorithm across different maskable sets for $l=400$, $600$, $800$, and $1000$. $T _{1}$, $T _{2}$, $T _{3}$, and $T _{4}$ correspond to the maskable sets $\mathcal{C}_{0}^{0}\left(\left|\left(\frac{\pi }{3} , \frac{\pi }{4} \right)\right\rangle\right)$, $\mathcal{C}_{\frac{\pi }{4}}^{\frac{\pi }{4}}\left(\left|\left(\frac{\pi }{3} , \frac{\pi }{4} \right)\right\rangle\right)$, $\mathcal{C}_{0}^{\frac{\pi }{2}}\left(\left|\left(\frac{\pi }{3} , \frac{\pi }{4} \right)\right\rangle\right)$, and $\mathcal{C}_{\frac{\pi }{3}}^{\frac{\pi }{3}}\left(\left|\left(\frac{2\pi }{3} , \frac{\pi }{5} \right)\right\rangle\right)$ respectively.
• Figure 3: The AUC of the XGBoost algorithm across different maskable sets for $l=400$, $600$, $800$, and $1000$. $T _{1}$, $T _{2}$, $T _{3}$, and $T _{4}$ correspond to the maskable sets $\mathcal{C}_{0}^{0}\left(\left|\left(\frac{\pi }{3} , \frac{\pi }{4} \right)\right\rangle\right)$, $\mathcal{C}_{\frac{\pi }{4}}^{\frac{\pi }{4}}\left(\left|\left(\frac{\pi }{3} , \frac{\pi }{4} \right)\right\rangle\right)$, $\mathcal{C}_{0}^{\frac{\pi }{2}}\left(\left|\left(\frac{\pi }{3} , \frac{\pi }{4} \right)\right\rangle\right)$, and $\mathcal{C}_{\frac{\pi }{3}}^{\frac{\pi }{3}}\left(\left|\left(\frac{2\pi }{3} , \frac{\pi }{5} \right)\right\rangle\right)$ respectively.
• Figure 4: An iteration cycle of the AL-XGBoost. Apply the XGBoost algorithm to the labeled training set $\mathcal{L}_i$ to predict samples in the unlabeled pool $\mathcal{U}_i$. Then select 5 samples using the hybrid query strategy and present them to the oracle for labeling. Add the queried samples to the labeled training set $\mathcal{L}_i$ to obtain $\mathcal{L}_{i+1}$, while simultaneously removing these queried samples from $\mathcal{U}_i$ to obtain $\mathcal{U}_{i+1}$. Starting from $i = 0$, iterate the above steps $n$ times.
• Figure 5: Different maskable sets in the Bloch sphere. $MT _{1}$, $MT _{2}$, $MT _{3}$, and $MT _{4}$ correspond to the maskable sets $\mathcal{D}_{\frac{\pi }{3}}^{\frac{\pi }{3}}\left((\frac{1}{4}, \frac{1}{4}, \frac{1}{4})\right)$, $\mathcal{D}_{\frac{2\pi }{3}}^{\frac{5\pi }{4}}\left((-\frac{1}{3}, -\frac{1}{2}, \frac{1}{5})\right)$, $\mathcal{D}_{\frac{\pi }{4}}^{\frac{3\pi }{4}}\left((\frac{1}{3}, \frac{1}{2}, -\frac{1}{4})\right)$, and $\mathcal{D}_{\frac{3\pi }{4}}^{\frac{5\pi }{3}}\left((-\frac{1}{4}, -\frac{1}{3}, -\frac{1}{5})\right)$ respectively.