Boosting device-independent cryptography with tripartite nonlocality

TL;DR

This paper explores how tripartite nonlocal correlations can enhance device-independent cryptography protocols, demonstrating improved performance over bipartite methods and analyzing the role of multipartite entanglement.

Contribution

It introduces tripartite Bell inequality-based protocols for DICKA and DIRE, providing analytical bounds on entropy and showing their advantages over bipartite protocols.

Findings

Tripartite protocols outperform bipartite ones in key rate and randomness generation.

Genuine multipartite entanglement is not necessary for DIRE protocols.

Analytical and numerical bounds on entropy for various tripartite Bell inequalities.

Abstract

Device-independent (DI) protocols, such as DI conference key agreement (DICKA) and DI randomness expansion (DIRE), certify private randomness by observing nonlocal correlations when two or more parties test a Bell inequality. While most DI protocols are restricted to bipartite Bell tests, harnessing multipartite nonlocal correlations may lead to better performance. Here, we consider tripartite DICKA and DIRE protocols based on testing multipartite Bell inequalities, specifically: the Mermin-Ardehali-Belinskii-Klyshko (MABK) inequality, and the Holz and the Parity-CHSH inequalities introduced in the context of DICKA protocols. We evaluate the asymptotic performance of the DICKA (DIRE) protocols in terms of their conference key rate (net randomness generation rate), by deriving lower bounds on the conditional von Neumann entropy of one party's outcome and two parties' outcomes. For the Holz inequality, we prove a tight analytical lower bound on the one-outcome entropy and conjecture a tight lower bound on the two-outcome entropy. We additionally re-derive the analytical one-outcome entropy bound for the MABK inequality with a much simpler method and obtain a numerical lower bound on the two-outcome entropy for the Parity-CHSH inequality. Our simulations show that DICKA and DIRE protocols employing tripartite Bell inequalities can significantly outperform their bipartite counterparts. Moreover, we establish that genuine multipartite entanglement is not a precondition for multipartite DIRE while its necessity for DICKA remains an open question.