The authors enumerate all local-Clifford orbits of qutrit graph states up to seven particles and show that orbit graph properties track the Schmidt measure.
Algorithm to Verify Local Equivalence of Stabilizer States
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abstract
We present an algorithm for verifying the local unitary (LU) equivalence of graph and stabilizer states. Our approach reduces the problem to solving a system of linear equations in modular arithmetic. Furthermore, we demonstrate that any LU transformation between two graph states takes a specific form, naturally generalizing the class of local Clifford (LC) transformations. Lastly, using existing libraries, we verify that for up to $n=11$, the number of LU and LC orbits of stabilizer states is identical.
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Orbit classification and analysis of qutrit graph states under local complementation and local scaling
The authors enumerate all local-Clifford orbits of qutrit graph states up to seven particles and show that orbit graph properties track the Schmidt measure.