Graphical Rigidity of Continuous Variable Graph States under Gaussian Local Transformations

arXiv:2610.31933v1 Announce Type: new Abstract: Multimode entangled pure Gaussian states are an essential resource for continuous variable (CV) quantum information processing. Menicucci et al. [2011] have shown how to describe them as graphs with complex adjacency matrices. Among such complex graph states (CGSs), quantum optics experimental setups straightforwardly display correlations described by purely imaginary graph states (iRGSs) whereas theoretical literature favors off-diagonal real graph state (RGS) descriptions, which actually reflect the entanglement structure in the infinite squeezing limit [Gonzalez-Arciniegas et al. 2021].