The impossibility of non-signaling privacy amplification

TL;DR

This paper proves that privacy amplification cannot be achieved in non-signaling quantum key distribution protocols when considering the most significant non-local behaviors, highlighting fundamental limitations in secure quantum communication.

Contribution

It demonstrates the impossibility of privacy amplification in non-signaling quantum protocols for key agreement, even with arbitrary hash functions and the most relevant non-local behaviors.

Findings

Privacy amplification is impossible for the most relevant non-local behaviors.

The result applies to arbitrary hash functions in non-signaling quantum protocols.

Shows fundamental limitations in secure quantum key agreement protocols.

Abstract

Barrett, Hardy, and Kent have shown in 2005 that protocols for quantum key agreement exist the security of which can be proven under the assumption that quantum or relativity theory is correct. More precisely, this is based on the non-local behavior of certain quantum systems, combined with the non-signaling postulate from relativity. An advantage is that the resulting security is independent of what (quantum) systems the legitimate parties' devices operate on: they do not have to be trusted. Unfortunately, the protocol proposed by Barrett et al. cannot tolerate any errors caused by noise in the quantum channel. Furthermore, even in the error-free case it is inefficient: its communication complexity is Theta(1/epsilon) when forcing the attacker's information below epsilon, even if only a single key bit is generated. Potentially, the problem can be solved by privacy amplification of relativistic - or non-signaling - secrecy. We show, however, that such privacy amplification is impossible with respect to the most important form of non-local behavior, and application of arbitrary hash functions.