Security proof for cryptographic protocols based only on the monogamy of Bell's inequality violations

TL;DR

This paper demonstrates that the monogamy of Bell's inequality violations, a weaker condition than no-signaling, suffices to prove the security of quantum key distribution across various theories, expanding the understanding of quantum security foundations.

Contribution

It establishes security proofs based solely on monogamy constraints, even in theories that violate no-signaling, broadening the scope of quantum cryptography security assumptions.

Findings

Monogamy of Bell violations suffices for security

Some non-no-signaling theories enable secure communication

Existing QKD protocols' security is qualitatively supported

Abstract

We show that monogamy of Bell's inequality violations, which is strictly weaker condition than no-signaling is enough to prove security of quantum key distribution. We derive our results for a whole class of monogamy constraints and generalize our results to any theory that communicating parties may have access to. Some of these theories do not respect no-signaling principle yet still allow for secure communication. This proves that no-signaling is only a sufficient condition for the possibility of secure communication, but not the necessary one. We also present some new qualitative results concerning the security of existing quantum key distribution protocols.