Randomness versus Nonlocality in Multi-input and Multi-output Quantum Scenario

TL;DR

This paper investigates the relationship between Bell nonlocality and quantum randomness certification in multi-input, multi-output scenarios, demonstrating that certain Bell inequalities can certify randomness and improving device-independent random number generation.

Contribution

It proves and experimentally verifies that violating any two-input Bell inequality certifies randomness, and explores the conditions under which multi-input Bell inequalities certify randomness.

Findings

Violating two-input Bell inequalities is necessary and sufficient for randomness certification.

Salavrakos-Augusiak-Tura-Wittek-Acín-Pironio inequalities can always certify randomness.

Achieved a randomness generation rate of 1.867 bits per photon pair.

Abstract

Device-independent randomness certification based on Bell nonlocality does not require any assumptions about the devices and therefore provides adequate security. Great effort has been made to demonstrate that nonlocality is necessary for generating quantum randomness, but the minimal resource required for random number generation has not been clarified. Here we first prove and experimentally demonstrate that violating any two-input Bell inequality is both necessary and sufficient for certifying randomness, however, for the multi-input cases, this sufficiency ceases to apply, leading to certain states exhibiting Bell nonlocality without the capability to certify randomness. We examine two typical classes of Bell inequalities with multi-input and multi-output, the facet inequalities and Salavrakos-Augusiak-Tura-Wittek-Ac\'in-Pironio Bell inequalities, in the high-dimensional photonic system, and observe the violation of the latter one can always certify randomness which is not true for the former. The private randomness with a generation rate of 1.867\pm0.018 bits per photon pair is obtained in the scenario of Salavrakos-Augusiak-Tura-Wittek-Ac\'in-Pironio Bell inequalities with 3-input and 4-output. Our work unravels the internal connection between randomness and nonlocality, and effectively enhances the performance of tasks such as device-independent random number generation.