The qudit Pauli group: non-commuting pairs, non-commuting sets, and structure theorems

Understand

Qudits with local dimension $d>2$ can have unique structure and uses that qubits ($d=2$) cannot.

• Qudit Pauli operators provide a very useful basis of the space of qudit states and operators.
• We study the structure of the qudit Pauli group for any, including composite, $d$ in several ways.
• To cover composite values of $d$, we work with modules over commutative rings, which generalize the notion of vector spaces over fields.