Batch Entanglement Detection in Parameterized Qubit States using Classical Bandit Algorithms

TL;DR

This paper introduces a novel batch entanglement detection method for two-qubit states using classical bandit algorithms, providing theoretical guarantees and demonstrating effectiveness through simulations and experiments.

Contribution

It connects batch entanglement detection with a Thresholding Bandit problem, enabling the use of classical machine learning techniques with proven measurement complexity bounds.

Findings

Method conclusively detects entanglement in a class of two-qubit states.

The approach offers theoretical guarantees on measurement/sample complexity.

Numerical and experimental results validate the effectiveness of the method.

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. [Phys. Rev. Lett., 116, 230501 (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 for performing batch entanglement detection by measuring a single-parameter family of entanglement witnesses, as proposed by Zhu, Teo, and Englert [Phys. Rev. A, 81, 052339, 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 a practically well-motivated class of two-qubit states $\mathcal{F}$, which includes 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.