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Geometric local invariants and pure three-qubit states

Geometric local invariants and pure three-qubit states

We explore a geometric approach to generating local $\text{SU}(2)$ and $\text{SL}(2,\mathbb{C})$ invariants for a collection of qubits inspired by lattice gauge theory. Each local invariant or ``gauge'' invariant is associated with a distinct closed path (or plaquette) joining some or all of the qubits. In lattice gauge theory, the lattice …