Quantifying Quantum Steering with Limited Resources: A Semi-supervised Machine Learning Approach

TL;DR

This paper introduces a semi-supervised machine learning method to efficiently quantify quantum steering using limited measurement data, reducing resource requirements compared to traditional SDP-based approaches.

Contribution

It presents a novel semi-supervised self-training model that estimates quantum steering without full state tomography, leveraging measurement probabilities for resource-efficient analysis.

Findings

High accuracy in estimating steerable weight with limited labeled data

Reduced resource consumption by avoiding full quantum state tomography

Robust generalization across different quantum states

Abstract

Quantum steering, an intermediate quantum correlation lying between entanglement and nonlocality, has emerged as a critical quantum resource for a variety of quantum information processing tasks such as quantum key distribution and true randomness generation. The ability to detect and quantify quantum steering is crucial for these applications. Semi-definite programming (SDP) has proven to be a valuable tool to quantify quantum steering. However, the challenge lies in the fact that the optimal measurement strategy is not priori known, making it time-consuming to compute the steerable measure for any given quantum state. Furthermore, the utilization of SDP requires full information of the quantum state, necessitating quantum state tomography, which can be complex and resource-consuming. In this work, we utilize the semi-supervised self-training model to estimate the steerable weight, a pivotal measure of quantum steering. The model can be trained using a limited amount of labeled data, thus reducing the time for labeling. The features are constructed by the probabilities derived by performing three sets of projective measurements under arbitrary local unitary transformations on the target states, circumventing the need for quantum tomography. The model demonstrates robust generalization capabilities and can achieve high levels of precision with limited resources.