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.

翻译：图态验证协议允许多方共享一个图态，同时检查该态是否被诚实制备，即使存在恶意方。由于图态是众多量子协议的起点，确保图态验证协议能够安全地与其他协议组合至关重要，这一性质被称为组合安全性。先前的工作[YDK21]推测，在抽象密码学框架内无法证明此类性质：我们通过证明所有图态验证协议均可转化为关于图态制备的自然功能性的组合安全协议，推翻了这一猜想。此外，我们表明，任何未修改的图态验证协议也可被视为对于略微不同但有用的功能性具有组合安全性。最后，我们证明这两个结果是最优的，即任何考虑任意黑盒协议的此类通用结果，要么必须修改协议，要么必须考虑不同的功能性。在此过程中，我们展示了一个将纠缠交换推广到任意图态的协议，该协议可能具有独立的研究价值。