  It is well known that the C*-algebra of an ordered pair of qubits is M_2 (x)
M_2. What about unordered pairs? We show in detail that M_3 (+) C is the
C*-algebra of an unordered pair of qubits. Then we use Schur-Weyl duality to
characterize the C*-algebra of an unordered n-tuple of d-level quantum systems.
Using some further elementary representation theory and number theory, we
characterize the quantum cycles. We finish with a characterization of the von
Neumann algebra for unordered words.
