AI 中文总结
本文引入逐个猜测（OTG）游戏作为研究多体纠缠有用性的新框架，发现其在泡利测量场景中可使获胜概率至少提高4%，且游戏价值遵循玩家选择概率分布的优超顺序。
AI 中文摘要
多体纠缠仍然是量子信息领域中具有挑战性且尚未完全理解的方面。纠缠一夫一妻制（Monogamy-of-Entanglement, MoE）游戏在研究由一夫一妻制约束施加的纠缠有用性限制方面非常有效。为了更好地揭示多体纠缠能够发挥作用的程度，我们引入了一类量子猜测游戏，称为逐个猜测（One-at-a-Time Guessing, OTG）游戏。在这些游戏中，量子玩家各自猜测裁判对预先共享的纠缠态进行随机测量的结果。与MoE游戏不同，OTG游戏根据指定的概率分布随机逐个选择玩家，从而探究每个玩家与裁判的关联。我们表明，尽管存在一夫一妻制约束，共享某些纠缠态的玩家仍能适度胜过仅依赖经典不确定性的玩家。这种优势甚至在仅涉及对量子比特进行泡利（Pauli）测量的简单OTG游戏中也会出现，其中最优纠缠使获胜概率至少提高4%。这与MoE游戏形成对比，在MoE游戏的多种场景中，共享纠缠被证明仅能提供有限的（若有的话）优势，相比经典策略。我们进一步确立了一个 majorization（优超）性质：OTG游戏的价值遵循玩家选择概率分布的优超顺序。我们还详细分析了一个两人OTG游戏，其中裁判对量子比特测量三个泡利可观测量中的一个，表明使用特定参数化的三量子比特W类态家族可实现最优玩法。这些结果表明，OTG游戏为研究多体量子关联中多体纠缠的有用性提供了一个有用的框架。
英文摘要
Multipartite entanglement remains a challenging and not fully understood aspect of quantum information. Monogamy-of-Entanglement (MoE) games have been highly effective for studying limitations on the usefulness of entanglement imposed by monogamy constraints. To better reveal the extent to which multipartite entanglement can be useful, we introduce a class of quantum guessing games, termed One-at-a-Time Guessing (OTG) games. In these games, quantum players individually guess the outcomes of random measurements performed by a referee on a pre-shared entangled state. Unlike MoE games, OTG games select players individually at random according to a specified probability distribution, thereby probing each player's correlation with the referee. We show that, despite monogamy constraints, players sharing certain entangled states can moderately outperform those relying only on classical uncertainty. This advantage arises even in simple OTG games involving only Pauli measurements on qubits, where optimal entanglement increases the winning probability by at least 4%. This contrasts with MoE games, where shared entanglement has been shown in several settings to provide only limited (if any) advantage over classical strategies. We further establish a majorization property: the value of an OTG game respects the majorization ordering of the player-selection probability distribution. We also analyze in detail a two-player OTG game in which the referee measures one of the three Pauli observables on a qubit, and show that it is optimally played using a specific parameterized family of three-qubit $W$-like states. These results suggest that OTG games provide a useful framework for investigating the usefulness of multipartite entanglement in multiparty quantum correlations.
Comments38 pages, 5 figures. Supplemental Code can be found at https://github.com/mas991/One-at-a-Time-Guessing-Games
