# Device-independent randomness generation with sublinear shared quantum resources

## TL;DR

This paper introduces a device-independent quantum random number generation protocol that efficiently produces near-linear bits of randomness using only a sublinear amount of shared entanglement, reducing quantum resource requirements.

## Contribution

It presents a novel DIRNG protocol that generates nearly n bits of randomness from n weakly entangled qubits, with sublinear entanglement scaling, minimizing quantum communication.

## Key findings

- Produces approximately n bits of randomness from n weakly entangled qubits.
- Requires only a sublinear number of singlet states relative to the number of bits generated.
- Enables DI protocols with minimal quantum communication between distant labs.

## Abstract

In quantum cryptography, device-independent (DI) protocols can be certified secure without requiring assumptions about the inner workings of the devices used to perform the protocol. In order to display nonlocality, which is an essential feature in DI protocols, the device must consist of at least two separate components sharing entanglement. This raises a fundamental question: how much entanglement is needed to run such DI protocols? We present a two-device protocol for DI random number generation (DIRNG) which produces approximately $n$ bits of randomness starting from $n$ pairs of arbitrarily weakly entangled qubits. We also consider a variant of the protocol where $m$ singlet states are diluted into $n$ partially entangled states before performing the first protocol, and show that the number $m$ of singlet states need only scale sublinearly with the number $n$ of random bits produced. Operationally, this leads to a DIRNG protocol between distant laboratories that requires only a sublinear amount of quantum communication to prepare the devices.