AI 中文总结
该研究给出泡利期望值二次式构成 n 量子比特纯态不变量族，推广了两量子比特‘五边形恒等式’，借助新工具实现多量子比特推广，揭示新结构性质，相关分析见配套论文。
AI 中文摘要
我们给出了一族泡利期望值的二次式，并证明它们构成了所有 n 量子比特纯态的与态无关的不变量。这个族推广了在[P. A. Höhn, Quantum 1, 38 (2017), P. A. Höhn 和 C. S. P. Wever, Phys. Rev. A 95, 012102 (2017)]的重构程序中发现的两量子比特‘五边形恒等式’，该恒等式刻画了纯态空间以及酉群，并在布鲁克纳 - 蔡林格信息测度中被解释为互补等式。推广到任意多个量子比特并非易事，因为需要新工具，这些新工具反过来揭示了两量子比特情形中不存在的新结构性质。在两篇配套论文中可以找到对这些性质及其与 n 量子比特泡利群中的相互无偏性和互补性的关系的全面分析。
英文摘要
We present a family of quadratics in Pauli expectation values, and prove that they constitute state-independent invariants for all n-qubit pure states. This family generalises the two-qubit `pentagon identities', discovered in the reconstruction programme of [P. A. Höhn, Quantum 1, 38 (2017), P. A. Höhn and C. S. P. Wever, Phys. Rev. A 95, 012102 (2017)], where they characterise the space of pure states, as well as the unitary group, and are interpreted as complementarity equalities in the Brukner-Zeilinger information measure. The generalisation to arbitrarily many qubits is nontrivial as it requires new tools which in turn reveal novel structural properties that are absent in the two-qubit case. A thorough analysis of these properties, and their relation with mutual unbiasedness and complementarity in the n-qubit Pauli group, can be found in two companion papers.
Comments5+7 pages; comments welcome
