Accumulation of Device-Independent Quantum Randomness against Time-Ordered No-Signalling Adversaries

TL;DR

This paper demonstrates that in device-independent quantum protocols, the min-entropy accumulates linearly over many runs against no-signalling adversaries, contrasting previous beliefs based on small sample analyses, and highlights the security implications in Bell test scenarios.

Contribution

It proves that min-entropy accumulates linearly for large n against no-signalling adversaries, resolving previous uncertainties from small n studies, and provides analytical and attack-based insights.

Findings

Min-entropy accumulates linearly for large n against no-signalling adversaries.

Analytical derivation of min-entropy for the Chained Bell test.

Class of attacks enabling perfect guessing of outputs in bipartite Pseudotelepathy games.

Abstract

The question of security of practical device-independent protocols against no-signalling adversaries, the ultimate form of cryptographic security, has remained open. A key ingredient is to identify how the entropy in the raw outputs of a Bell test accumulates over $n$ sequential runs (termed time-ordered no-signalling) against a no-signalling adversary. Previous numerical and analytical investigations for small $n$ ($\leq 5$) had suggested that the min-entropy might not accumulate linearly in contrast to the case of quantum adversaries. Here we point out that despite the findings for small $n$, the min-entropy does in fact accumulate linearly for large $n$. We illustrate the difference in randomness accumulation against quantum and no-signalling adversaries with the paradigmatic example of the Chained Bell test for which we analytically derive the min-entropy. Finally, we illustrate the power of the no-signalling adversary by providing a class of attacks that allow an eavesdropper to perfectly guess the outputs of one player in general bipartite Pseudotelepathy games.