Batch Entanglement Detection in Parameterized Qubit States using Classical Bandit Algorithms

TMLR Paper5355 Authors

Abstract: Entanglement is a key property of quantum states that acts as a resource for a wide range of tasks in quantum computing. Entanglement detection is a key conceptual and practical challenge. Without adaptive or joint measurements, entanglement detection is constrained by no-go theorems (Lu et al., 2016), necessitating full state tomography. Batch entanglement detection refers to the problem of identifying all entangled states from amongst a set of $K$ unknown states which finds applications in quantum information processing. We devise a method to perform batch entanglement detection by performing measurements derived from a single-parameter family of entanglement witnesses from Zhu et al. (2010), followed by a thresholding bandit algorithm on the measurement data. The proposed method can perform batch entanglement detection conclusively, when the unknown states are drawn from practically well-motivated class of two qubit states $\mathcal{F}$ that include Depolarised Bell states, Bell diagonal states etc. Our key novelty lies in drawing a connection between batch entanglement detection, and a Thresholding Bandit problem in classical Multi-Armed Bandits (MAB). The connection to the MAB problem also enables us to derive theoretical guarantees on the measurement/sample complexity of the proposed technique. We demonstrate the performance of the proposed method through numerical simulations and an experimental implementation. More broadly, this paper highlights the potential for employing classical machine learning techniques for quantum entanglement detection.

Submission Length: Long submission (more than 12 pages of main content)

Assigned Action Editor: ~Arya_Mazumdar1

Submission Number: 5355