一般概率理论中态的反可区分性
Antidistinguishability of states in General Probabilistic Theories
- Indian Institute of Technology Bhubaneswar（印度技术研究所布巴内斯瓦尔分校）
- S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国家中心）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文在一般概率理论中研究态的反可区分性，提出精细定义并推导上界，证明多边形模型中纯态可反区分，且某些多边形模型可超越最优量子值。
中文摘要 AI 辅助
我们在一般概率理论（GPTs）框架内研究态的反可区分性。我们将反可区分性、强反可区分性和等反可区分性定义为对测量效应施加额外约束的精细概念。我们建立了关于这些反可区分性概念的一般性结果，并推导出等反可区分集合的基数上界，该上界以态空间的仿射维数表示。随后，我们在多边形理论中研究反可区分性，得到了态集合反可区分的条件。因此，我们证明了多边形模型中所有纯态的集合是可反区分的。此外，我们识别出强反可区分态和等反可区分态的广泛族类。最后，利用随机排除码（其成功概率由不同编码态集合的反可区分性决定），我们探测了多边形理论的非经典性。我们发现某些多边形模型可以超越最优量子值，而其最优性能在大多边形极限下收敛于量子极限。
英文摘要
We investigate antidistinguishability of states within the framework of general probabilistic theories (GPTs). We formulate antidistinguishability, strong and equal antidistinguishability as refined notions that imposed additional constraint on the measurement effects. We establish general results relating these notions of antidistinguishability and derive an upper bound on the cardinality of equally antidistinguishable sets in terms of the affine dimension of the state space. We then study antidistinguishability in polygonal theories, obtaining conditions for antidistinguishability of a set of states. In consequence, we show that the set of all pure states in a polygon model is antidistinguishable. Additionally, we identify broad families of strongly and equally antidistinguishable states. Finally, using Random Exclusion Codes, whose success probability is governed by the antidistinguishability of different sets of encoding states, we probe the nonclassicality of polygon theories. We find that certain polygon models can outperform the optimal quantum value, while their optimal performance converges to the quantum limit in the large-polygon limit.
