AI 中文总结
研究 n 量子比特泡利群中简并可观测量的互补性，通过获取可观测量互补准则、联系互补集与信息纯态互补等式，证明互补集蕴含强熵不确定性关系。
AI 中文摘要
量子力学中的可观测量通常是互补的，即它们揭示了关于给定系统的相互不兼容的信息片段。这一性质不仅是量子形式主义的基本信条，也是量子密码协议的关键组成部分。因此，引发了许多关于寻找高度互补可观测量集的研究。在本文中，我们考虑最强形式，即互补可观测量之间的信息不仅不兼容而且相互排斥。已知在素数幂维系统（如 n 量子比特系统）中存在最大的非简并互补可观测量集。我们研究简并可观测量的互补性，具体证明与 n 量子比特泡利群相关的可观测量在此限制下也表现出互补性：首先，我们得到两个这样的可观测量互补的一个准则；其次，我们将最大互补可观测量集与信息纯态互补等式联系起来，这在两篇配套论文中进一步研究。等价地，这些结果可以用泡利群的（不一定是最大的）阿贝尔子群的最大互补集与（可能是粗粒化的）相互无偏基联系起来表述。最后，我们证明这些互补集蕴含强熵不确定性关系。
英文摘要
Observables in quantum mechanics are generally complementary, that is, they reveal mutually incompatible pieces of information about a given system. This property is not only a fundamental tenet of the quantum formalism, but also a key component in quantum cryptographic protocols. As such it has fuelled much research into finding sets of highly complementary observables. In its strongest form -- the one we consider in this work -- the information between complementary observables is not merely incompatible but mutually exclusive: maximal information about one observable implies no information about the other, and vice versa. Maximal sets of non-degenerate complementary observables are known to exist in systems of prime power dimension such as n-qubit systems. Here, we study complementarity of degenerate observables, specifically we prove that observables associated with the n-qubit Pauli group also exhibit complementarity under this restriction: first, we obtain a criterion for two such observables to be complementary and, second, we relate maximal sets of complementary observables with informational pure state complementarity equalities, further studied in two companion papers. Equivalently, these results can be formulated in terms of maximal complementary sets of (not necessarily maximal) Abelian subgroups of the Pauli group linking with (possibly coarse-grained) mutually unbiased bases. Finally, we prove that these complementarity sets entail strong entropic uncertainty relations.
Comments5+9 pages; comments welcome
