Graphical Rigidity of Continuous Variable Graph States under Gaussian Local Transformations
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]. We study them beyond this ideal case, thus establishing in the finite squeezing regime an equivalence criterion for the generic case of CGSs through a graph propagating set of conditions which either finds a Gaussian Local Unitary (GLU) converting one state to another or gives a proof of impossibility if such a GLU does not exist. In the experimentally relevant case of the conversion between iRGSs and RGSs, the set of conditions results in simple relations between the topologies of the equivalent real and imaginary graphs. Finally, we show that the canonical forms of iRGSs and RGSs imply that the topology of the CV real and imaginary graph states are too rigid to admit any exact qumode local-addition analogue to the qubit complementation or qudit local-addition, thus demonstrating the non-existence of any exact qumode local-addition for these states. We however define an approximate one when the squeezing is strong enough.
Related
- Temporal limitations and digital data processing in continuous variable measurements of non-Gaussian states
- A phase-space approach for performing continuous-variable quantum teleportation with a non-Gaussian resource
- Efficient Simulation of Hybrid Continuous- and Discrete-Variable Quantum Circuits via Gaussian Decompositions
- Delta-sigma noise shaping for low-resolution quantization in Gaussian-modulated continuous-variable quantum key distribution
- Effect of molybdenum content on phase transformations during continuous heating of metastable β Ti-Mo alloys
BibTeX
@misc{ciliberto2026graphical,
title = {{Graphical Rigidity of Continuous Variable Graph States under Gaussian Local Transformations}},
author = {Giorgio Ciliberto and Frédéric Grosshans},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31933},
eprint = {2610.31933},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05839002v1},
}
RIS
TY - UNPB
TI - Graphical Rigidity of Continuous Variable Graph States under Gaussian Local Transformations
AU - Giorgio Ciliberto
AU - Frédéric Grosshans
PY - 2026
DA - 2026/10/22
PB - HAL
DO - 10.48550/arxiv.2610.31933
UR - https://hal.science/hal-05839002v1
AB - 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]. We study them beyond this ideal case, thus establishing in the finite squeezing regime an equivalence criterion for the generic case of CGSs through a graph propagating set of conditions which either finds a Gaussian Local Unitary (GLU) converting one state to another or gives a proof of impossibility if such a GLU does not exist. In the experimentally relevant case of the conversion between iRGSs and RGSs, the set of conditions results in simple relations between the topologies of the equivalent real and imaginary graphs. Finally, we show that the canonical forms of iRGSs and RGSs imply that the topology of the CV real and imaginary graph states are too rigid to admit any exact qumode local-addition analogue to the qubit complementation or qudit local-addition, thus demonstrating the non-existence of any exact qumode local-addition for these states. We however define an approximate one when the squeezing is strong enough.
ER -