论文标题
量子力学？这一切都是有趣的，并且游戏失去了$ i $
Quantum mechanics? It's all fun and games until someone loses an $i$
论文作者
论文摘要
QBISM将量子力学视为概率理论的补充。该增加为与实验环境中赌博有关的决策代理提供了一个额外的规范规则，这与双缝实验类似。从Qbist的角度来确定了天生规则的含义。此外，它表明，制定基础讨论的诞生规则的最佳方法是关于信息完整的参考设备。最近的工作[DeBrota，Fuchs和Stacey，Phys。 Rev. Res。 2，013074（2020）]证明，采用对称信息完整的POVM（或SICS）的参考设备达到了最小的量子：它们见证了经典和量子之间的不可约定差异。在本文中，我们试图回答有关房地产空间量子理论的类似问题。尽管标准的量子力学似乎使SIC在所有有限的维度中都存在，但在量子理论的情况下，众所周知，SIC在大多数维度中都不存在。因此，我们试图在第一个实际维度中识别最佳参考设备，而没有SIC（即$ d = 4 $），以期更好地理解复数在量子力学中的基本作用。与它们的复杂对应物相反，导致Qbist对房地产空间量子理论的理解的表达令人惊讶地复杂。
QBism regards quantum mechanics as an addition to probability theory. The addition provides an extra normative rule for decision-making agents concerned with gambling across experimental contexts, somewhat in analogy to the double-slit experiment. This establishes the meaning of the Born Rule from a QBist perspective. Moreover it suggests that the best way to formulate the Born Rule for foundational discussions is with respect to an informationally complete reference device. Recent work [DeBrota, Fuchs, and Stacey, Phys. Rev. Res. 2, 013074 (2020)] has demonstrated that reference devices employing symmetric informationally complete POVMs (or SICs) achieve a minimal quantumness: They witness the irreducible difference between classical and quantum. In this paper, we attempt to answer the analogous question for real-vector-space quantum theory. While standard quantum mechanics seems to allow SICs to exist in all finite dimensions, in the case of quantum theory over the real numbers it is known that SICs do not exist in most dimensions. We therefore attempt to identify the optimal reference device in the first real dimension without a SIC (i.e., $d=4$) in hopes of better understanding the essential role of complex numbers in quantum mechanics. In contrast to their complex counterparts, the expressions that result in a QBist understanding of real-vector-space quantum theory are surprisingly complex.
