Entanglement is a key resource for a wide range of tasks in quantum information and computing. Thus, verifying availability of this quantum resource is essential. Extensive research on entanglement detection has led to no-go theorems (Lu et al. [Phys. Rev. Lett., 116, 230501 (2016)]) that highlight the need for full state tomography (FST) in the absence of adaptive or joint measurements. Recent advancements, as proposed by Zhu, Teo, and Englert [Phys. Rev. A, 81, 052339, 2010], introduce a single-parameter family of entanglement witness measurements which are capable of conclusively detecting certain entangled states and only resort to FST when all witness measurements are inconclusive. We find a variety of realistic noisy two-qubit quantum states $\mathcal{F}$ that yield conclusive results under this witness family. We solve the problem of detecting entanglement among $K$ quantum states in $\mathcal{F}$, of which $m$ states are entangled, with $m$ potentially unknown. We recognize a structural connection of this problem to the Bad Arm Identification problem in stochastic Multi-Armed Bandits (MAB). In contrast to existing quantum bandit frameworks, we establish a new correspondence tailored for entanglement detection and term it the $(m,K)$-quantum Multi-Armed Bandit. We implement two well-known MAB policies for arbitrary states derived from $\mathcal{F}$, present theoretical guarantees on the measurement/sample complexity and demonstrate the practicality of the policies through numerical simulations. More broadly, this paper highlights the potential for employing classical machine learning techniques for quantum entanglement detection.

翻译：纠缠是量子信息与计算中众多任务的关键资源，因此验证这一量子资源的可用性至关重要。纠缠检测的广泛研究已催生了一些不可行性定理（Lu等人[Phys. Rev. Lett., 116, 230501 (2016)]），这些定理强调了在缺乏自适应或联合测量的情况下必须进行完整态层析。Zhu、Teo和Englert近期提出的进展[Phys. Rev. A, 81, 052339, 2010]引入了一个单参数族的纠缠见证测量，该族测量能够确定性地检测某些纠缠态，仅在所有见证测量均无法判定时才需进行完整态层析。我们发现了多种现实噪声双量子比特态$\mathcal{F}$，在该见证族下能产生确定性检测结果。我们解决了从$\mathcal{F}$中$K$个量子态（其中$m$个为纠缠态，$m$可能未知）中检测纠缠的问题。我们认识到该问题与随机多臂赌博机中的坏臂识别问题存在结构关联。与现有量子赌博机框架不同，我们建立了一种专为纠缠检测定制的新对应关系，并将其命名为$(m,K)$-量子多臂赌博机。我们针对从$\mathcal{F}$导出的任意态实现了两种经典的多臂赌博机策略，给出了测量/样本复杂度的理论保证，并通过数值模拟验证了策略的实用性。更广泛而言，本文揭示了运用经典机器学习技术进行量子纠缠检测的潜力。