费米子与实数量子理论中的Tsirelson问题

中文摘要 AI 辅助

在先前的工作中，我们证明了实数量子理论（RQT）在实验上无法与普通量子理论（QT）区分。在本文中，我们研究了这种不可区分性在两种自然的设定扩展下是否仍然成立：允许分离测量由对易而非张量积可观测量表示，以及施加超选择规则（如在费米子信息理论中那样）。我们表明在这两种情况下它都成立。我们的第一个结果是对RQT中Tsirelson问题的肯定回答：对易和张量积测量生成相同的有限维关联。这令人惊讶地并非标准复数证明的平凡推论，因为它不能直接推广到实数情形。证明中的障碍在存在超选择规则时变得尤为相关，这就是为什么我们首先在RQT中建立等价性，然后再将框架扩展到超选择RQT。我们的第二个结果是超选择理论的局部实数量子表述。我们扩展RQT框架以容纳实数上的超选择表示，并特别表明它允许一个费米子版本，其预测在实验上与费米子信息理论的预测不可区分。更一般地，该构造扩展到所有超选择量子理论。

英文摘要

In a previous work, we showed that real quantum theory (RQT) cannot be experimentally distinguished from ordinary quantum theory (QT). In this paper, we investigate whether this indistinguishability survives two natural extensions of the setting: allowing separated measurements to be represented by commuting rather than tensor-product observables, and imposing superselection rules, as in fermionic information theory. We show that it does in both cases. Our first result is a positive answer to the Tsirelson problem in RQT: commuting and tensor-product measurements generate the same finite-dimensional correlations. This is surprisingly not a trivial consequence of the standard complex proof, as it does not carry over to the reals. The proof obstruction becomes particularly relevant in the presence of superselection rules, which is why we first establish the equivalence in RQT before extending the framework to superselected RQT. Our second result is a local, real quantum formulation of superselected theories. We extend the RQT framework to accommodate a representation of superselection over the reals and show, in particular, that it admits a fermionic version whose predictions are experimentally indistinguishable from those of fermionic information theory. More generally, the construction extends to all superselected QTs.

发表机构

• Mathematical Institute, Slovak Academy of Sciences（斯洛伐克科学院数学研究所）
• ENS Lyon, Inria（里昂高等师范学院，法国国家信息与自动化研究所）

机构由 AI 辅助整理，请以论文原文为准。

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43 pages plus appendices