Certifying optimal device-independent quantum randomness in quantum networks

TL;DR

This paper introduces a new family of multipartite Bell inequalities inspired by the stabilizer group of GHZ states, enabling optimal device-independent quantum randomness certification and self-testing, especially effective with non-maximal Bell values.

Contribution

The authors propose a simple, scalable family of Bell inequalities for multipartite systems that improves randomness certification efficiency over existing inequalities like Mermin-type.

Findings

Achieves optimal quantum randomness certification with GHZ states.

Provides an analytical upper bound for the Holevo quantity.

Outperforms MABK, Parity-CHSH, and Holz inequalities at N=3.

Abstract

Bell nonlocality provides a device-independent (DI) way to certify quantum randomness, based on which true random numbers can be extracted from the observed correlations without detail characterizations on devices for quantum state preparation and measurement. However, the efficiency of current strategies for DI randomness certification is still heavily constrained when it comes to non-maximal Bell values, especially for multiple parties. Here, we present a family of multipartite Bell inequalities that allows to certify optimal quantum randomness and self-test GHZ (Greenberger-Horne-Zeilinger) states, which are inspired from the stabilizer group of the GHZ state. Due to the simple representation of stabilizer group for GHZ states, this family of Bell inequalities is of simple structure and can be easily expanded to more parties. Compared with the Mermin-type inequalities, this family of Bell inequality is more efficient in certifying quantum randomness when non-maximal Bell values achieved. Meanwhile, the general analytical upper bound for the Holevo quantity is presented, and achieves better performance compared with the MABK (Mermin-Ardehali-Belinskii-Klyshko) inequality, Parity-CHSH (Clauser-Horne-Shimony-Holt) inequality and Holz inequality at $N=3$, which is of particular interests for experimental researches on DI quantum cryptography in quantum networks.