Upper bound on the Guessing probability using Machine Learning

TL;DR

This paper explores the use of deep learning to estimate the guessing probability in quantum cryptography, addressing computational challenges in large systems and providing insights into nonlocal correlations.

Contribution

It introduces machine learning methods to approximate guessing probabilities in Bell scenarios, offering a scalable alternative to semi-definite programming.

Findings

Deep learning effectively estimates guessing probabilities.

Machine learning provides insights into quantum nonlocality.

Approach scales better than traditional SDP methods.

Abstract

The estimation of the guessing probability has paramount importance in quantum cryptographic processes. It can also be used as a witness for nonlocal correlations. In most of the studied scenarios, estimating the guessing probability amounts to solving a semi-definite programme, for which potent algorithms exist. However, the size of those programs grows exponentially with the system size, becoming infeasible even for small numbers of inputs and outputs. We have implemented deep learning approaches for some relevant Bell scenarios to confront this problem. Our results show the capabilities of machine learning for estimating the guessing probability and for understanding nonlocality.