论文标题
图理论的不确定性关系
Uncertainty relations from graph theory
论文作者
论文摘要
量子测量本质上是概率和量子理论，通常禁止准确预测同时测量的结果。通过不确定性关系捕获并量化了这种现象。尽管自量子理论的成立以来进行了研究，但一般而言，确定量子测量集合可能的期望值的问题仍然没有解决。通过在可观测值和图理论之间构建密切的联系，我们得出了对任何一组二分法可观察物有效的不确定性关系。在许多情况下，这些关系是紧密的，并且与相关图的最大集团的大小相关。作为应用，我们的结果可以直接用于制定熵不确定性关系，可分离性标准和纠缠证人。
Quantum measurements are inherently probabilistic and quantum theory often forbids to precisely predict the outcomes of simultaneous measurements. This phenomenon is captured and quantified through uncertainty relations. Although studied since the inception of quantum theory, the problem of determining the possible expectation values of a collection of quantum measurements remains, in general, unsolved. By constructing a close connection between observables and graph theory, we derive uncertainty relations valid for any set of dichotomic observables. These relations are, in many cases, tight, and related to the size of the maximum clique of the associated graph. As applications, our results can be straightforwardly used to formulate entropic uncertainty relations, separability criteria and entanglement witnesses.
