A lot of structural information on a set of Pauli strings can be gathered from the graph encoding its commutator and anti-commutator relations. We investigate a certain subclass of those for which important properties including uncertainty relations and the ground-state energy of a Hamiltonian can be directly linked to the weighted independence number of the corresponding frustration graph. We baptise this class of graphs ℏ-perfect as it includes the classes of perfect, and h-perfect graphs.

We not only investigate its behavior under typical graph operations and classify how common they are, but also use it to solve efficiency problems in shadow tomography.

许振朋教授，2013年至2018年于南开大学陈省身数学所理论物理室攻读博士学位，毕业后在德国锡根大学从事博士后工作，并获德国洪堡基金会支持。研究方向为量子力学基础问题和量子信息，专注于不同系统中的量子关联，从单体系统、少体系统到近期的网络系统。近五年发表Physical Review Letters 4篇，Nature Communications、Science Advances、PRX Quantum各1篇，并荣获奥地利科学院颁发的2021年度埃伦费斯特量子基础最佳论文奖。