Graph states of prime-power dimension from generalized CNOT quantum circuit

Understand

We construct multipartite graph states whose dimension is the power of a prime number.

• This is realized by the finite field, as well as the generalized controlled-NOT quantum circuit acting on two qudits.
• We propose the standard form of graph states up to local unitary transformations and particle permutations.
• The form greatly simplifies the classification of graph states as we illustrate up to five qudits.