一句话:将 GHZ 态上的 Mermin 型非局域性论证推广到一般情形,给出精确群论条件,并扩展量子秘密共享协议。
本文广泛推广 GHZ 态上的 Mermin 型非局域性论证,并给出实现非局域性的精确群论条件。作者在 dagger compact 范畴的 string diagram 图形语言中完成证明,使结论不限于量子理论,而适用于任何具备相应代数结构的理论。结果产生量子可实现的 All-vs-Nothing 论证层级,并用于非平凡扩展 Hillery–Bužek–Berthiaume 混合量子-经典秘密共享方案。评估以群论条件刻画和图形化证明为主,并借助协议应用展示有效性。
We broadly generalise Mermin-type arguments on GHZ states, and we provide exact group-theoretic conditions for non-locality to be achieved. Our results are of interest in quantum foundations, where they yield a new hierarchy of quantum-realisable All-vs-Nothing arguments. They are also of interest to quantum protocols, where they find immediate application to a non-trivial extension of the hybrid quantum-classical secret sharing scheme of Hillery, Bu\v{z}ek and Berthiaume (HBB). Our proofs are carried out in the graphical language of string diagrams for dagger compact categories, and their validity extends beyond quantum theory to any theory featuring the relevant algebraic structures.