Quantum theory and relativity are the pillar theories on which our understanding of physics is based. Poincaré invariance is a fundamental physical principle stating that the experimental results must be the same in all inertial reference frames in Minkowski spacetime. It is a basic condition imposed on quantum theory in order to construct quantum field theories, hence, it plays a fundamental role in the standard model of particle physics too. As is well known, Minkowski spacetime follows from clear physical principles, like the relativity principle and the invariance of the speed of light. Here we reproduce such a derivation but leave the number of spatial dimensions $n$ as a free variable. Then, assuming that spacetime is Minkowski in $1+n$ dimensions and within the framework of general probabilistic theories, we reconstruct the qubit Bloch ball and finite dimensional quantum theory, and obtain that the number of spatial dimensions must be $n=3$, from Poincaré invariance and other physical postulates. Our results suggest a fundamental physical connection between spacetime and quantum theory.

中文翻译：

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时空对称性和量子比特布洛赫球：有限维量子理论和空间维数的物理推导

量子理论和相对论是我们理解物理学的支柱理论。庞加莱不变性是一个基本的物理原理，它表明在闵可夫斯基时空的所有惯性参考系中，实验结果必须相同。它是强加于量子理论以构建量子场论的基本条件，因此，它在粒子物理学的标准模型中也起着基础性的作用。众所周知，闵可夫斯基时空遵循明确的物理原理，如相对性原理和光速不变性。这里我们重现了这样的推导，但留下了空间维度的数量$n$作为自由变量。那么，假设时空是闵可夫斯基$1+n$ 维数，在一般概率理论的框架内，我们重构了量子比特布洛赫球和有限维量子理论，得到空间维数必须是 $n=3$，来自庞加莱不变性和其他物理假设。我们的结果表明时空和量子理论之间存在基本的物理联系。