从割多胞体的面导出两方多二值可观测量的紧贝尔不等式
量子物理
2007-05-23 v3
摘要
先前被辨识的贝尔不等式族相对较少。若干例子为平凡不等式、CHSH、I_{mm22}及CGLMP不等式。本文给出大量多可观测情形下紧贝尔不等式的新族。例如,对于两方各含10个二值可观测量的情形,除CHSH外获得了44,368,793个不等价的紧贝尔不等式。这通过首先建立贝尔不等式与割多胞体(多面体组合中熟知的对象)的面之间的关系而达成。我们随后证明一定理,允许借助源自Fourier-Motzkin消去、我们称之为三角消去的过程,由较小多胞体的面导出割多胞体的新面。这些新面进而给出新紧贝尔不等式。我们给出了关于投影、提升及相应贝尔多胞体成员检测复杂度的附加结果。
引用
@article{arxiv.quant-ph/0404014,
title = {Deriving Tight Bell Inequalities for 2 Parties with Many 2-valued Observables from Facets of Cut Polytopes},
author = {David Avis and Hiroshi Imai and Tsuyoshi Ito and Yuuya Sasaki},
journal= {arXiv preprint arXiv:quant-ph/0404014},
year = {2007}
}
备注
24 pages, LaTeX. Asymmetric setting of observables is added in the introduction, section 5.4 and section 7.2. Some references and typos are corrected. A description on the I_{3422}^2 inequality is corrected in section 5.4 and added to section 5.1