发表机构
Newcastle University（纽卡斯尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究二能级系统中四个互无偏问题的存在性，指出在无算子乘积限制下可实现为hyperbit，但在两个量子比特内实现时缺乏某些性质，且被宇称超选择排除。
AI 中文摘要
两个尖锐的是/否问题互无偏，当且仅当它们的对合反对易。因此，一组无偏问题构成一个Clifford代数，其最大规模为奇数，这意味着四个反对易问题通常蕴含第五个：实数、复数和四元数量子理论的二能级系统分别允许两个、三个和五个问题，而四个被跳过。在没有这种算子乘积限制的情况下，具有四个无偏问题的二能级系统作为四维Bloch球（即hyperbit）存在。挑选出Jordan态空间的单系统假设允许这样的模型，只有能量可观测性将其排除。我们展示了它所缺乏的，并在两个量子比特内实现它：其Kirkwood-Dirac虚部是隐藏的$\mathfrak{so}(4)$生成元，其复合体允许纠缠但没有相互作用，其24胞腔态在退极化强度$2/3$以下保持Spekkens制备上下文性。用费米子术语来说，四个问题是两个模式的Majorana算子，而第五个是宇称：因此四问题系统是被宇称超选择移除的扇区。
英文摘要
Two sharp yes/no questions are mutually unbiased if and only if their involutions anticommute. A set of unbiased questions is therefore a Clifford algebra, whose maximal size is odd, meaning four anticommuting questions typically imply a fifth: the two-level systems of real, complex and quaternionic quantum theory allow two, three and five questions, while four is skipped. Without this operator product restriction, a two-level system with four unbiased questions exists as the four-dimensional Bloch ball, the hyperbit. The single-system postulates that pick out the Jordan state spaces allow such a model, and only energy observability rules it out. We show what it lacks, and realise it inside two qubits: its Kirkwood-Dirac imaginary parts are hidden $\mathfrak{so}(4)$ generators, its composites allow entanglement but no interaction, and its 24-cell of states stays Spekkens preparation contextual down to depolarising strength $2/3$. In fermionic terms, the four questions are the Majorana operators of two modes while the fifth is parity: the four-question system is therefore the sector removed by parity superselection.
Comments6+3 pages, no figures
