Classical Bandit Algorithms for Entanglement Detection in Parameterized Qubit States

• URL: http://arxiv.org/abs/2406.19738v1
• Date: Fri, 28 Jun 2024 08:26:47 GMT
• Title: Classical Bandit Algorithms for Entanglement Detection in Parameterized Qubit States
• Authors: Bharati. K, Vikesh Siddhu, Krishna Jagannathan,
• Abstract summary: Entanglement is a key resource for a wide range of tasks in quantum information and computing. This paper highlights the potential for employing classical machine learning techniques for quantum entanglement detection.
• Score: 3.5502600490147196
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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