Quantum secure learning with classical samples

TL;DR

This paper introduces a quantum-secure learning protocol using classical samples, leveraging quantum principles to ensure only legitimate learners can succeed, thus preventing adversaries in a hybrid quantum-classical setting.

Contribution

It proposes a novel hybrid sampling protocol with a security condition based on quantum no-broadcasting, ensuring secure learning independent of the learning algorithm.

Findings

Security condition derived from quantum no-broadcasting principle

Guarantees PAC learning with a lower sample bound

Prevents adversarial learners through an upper sample bound

Abstract

Studies addressing the question "Can a learner complete the learning securely?" have recently been spurred from the standpoints of fundamental theory and potential applications. In the relevant context of this question, we present a classical-quantum hybrid sampling protocol and define a security condition that allows only legitimate learners to prepare a finite set of samples that guarantees the success of the learning; the security condition excludes intruders. We do this by combining our security concept with the bound of the so-called probably approximately correct (PAC) learning. We show that while the lower bound on the learning samples guarantees PAC learning, an upper bound can be derived to rule out adversarial learners. Such a secure learning condition is appealing, because it is defined only by the size of samples required for the successful learning and is independent of the algorithm employed. Notably, the security stems from the fundamental quantum no-broadcasting principle. No such condition can thus occur in any classical regime, where learning samples can be copied. Owing to the hybrid architecture, our scheme also offers a practical advantage for implementation in noisy intermediate-scale quantum devices.