2026/06/03 by Xiaowei Huang, Fei Shi, Lijun Zhang +1
Chemistry · Computer Science · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Matroid #Matroid partitioning #Quantum #Quantum Information and Cryptography #Quantum entanglement #Quantum state #State (computer science) #Symmetry (geometry) #Topological Materials and Phenomena
paper · pdf · doi:10.1103/mx1w-k8fg
published in Physical Review A 113(6) (American Physical Society)
openalex publication_date 2026/06/03 · openalex created_date 2026/06/04 · openalex updated_date 2026/08/05
In this work, we establish a structural correspondence between quantum states and matroid theory. This connection demonstrates that key properties of quantum states, including entanglement and measurement, can be characterized in purely combinatorial terms via matroids, despite the apparent conceptual distance between these two fields. Using this framework, we show that a matroid-supported state is genuinely entangled when its underlying matroid is connected. Moreover, a uniform superposition over all bases of a matroid is genuinely entangled if and only if the matroid is connected. We also demonstrate that a local measurement in the Z-basis on such a state yields another matroid-supported state, whose underlying matroid is a minor of the original one. Inspired by matroid duality, we further propose a notion of quantum state duality, uncovering a deep structural symmetry in state transformations.