All graph state verification protocols are composably secure

TL;DR

This paper proves that all graph state verification protocols can be made securely composable, ensuring their safe integration into larger quantum protocols, and introduces a generalized entanglement swapping protocol.

Contribution

It disproves the conjecture that graph state verification cannot be proven composably secure within the abstract cryptography framework and provides a method to achieve this security.

Findings

All graph state verification protocols can be transformed into composably secure protocols.

Unchanged protocols are also secure for a slightly different functionality.

The results are proven to be optimal, with limitations on generalization.

Abstract

Graph state verification protocols allow multiple parties to share a graph state while checking that the state is honestly prepared, even in the presence of malicious parties. Since graph states are the starting point of numerous quantum protocols, it is crucial to ensure that graph state verification protocols can safely be composed with other protocols, this property being known as composable security. Previous works [YDK21] conjectured that such a property could not be proven within the abstract cryptography framework: we disprove this conjecture by showing that all graph state verification protocols can be turned into a composably secure protocol with respect to the natural functionality for graph state preparation. Moreover, we show that any unchanged graph state verification protocols can also be considered as composably secure for a slightly different, yet useful, functionality. Finally, we show that these two results are optimal, in the sense that any such generic result, considering arbitrary black-box protocols, must either modify the protocol or consider a different functionality. Along the way, we show a protocol to generalize entanglement swapping to arbitrary graph states that might be of independent interest.