The star-algebra \(M_2 \otimes M_2 \) models a pair of qubits.
We show in detail that \(M_{3} \oplus \mathbb{C}\) models an
*unordered* pair of qubits. Then we use the late 19th century
Schur-Weyl duality, to characterize the star-algebra that models
an unordered n-tuple of d-level quantum systems.

With more elementary Representation Theory and Number Theory, we characterize the quantum cycles. We finish with a characterization of the von Neumann algebra that models the unordered words.