The Foliage Partition: An Easy-to-Compute LC-Invariant for Graph States
arXiv:2305.07645 · doi:10.22331/q-2025-04-24-1720
Abstract
This paper introduces the foliage partition, an easy-to-compute LC-invariant for graph states, of computational complexity in the number of qubits. Inspired by the foliage of a graph, our invariant has a natural graphical representation in terms of leaves, axils, and twins. It captures both, the connection structure of a graph and the -body marginal properties of the associated graph state. We relate the foliage partition to the size of LC-orbits and use it to bound the number of LC-automorphisms of graphs. We also show the invariance of the foliage partition when generalized to weighted graphs and qudit graph states.
arXiv comment21 pages, 10 figures. Both authors contributed equally to this work
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