  This note presents a simple and unified formulation of the most fundamental
structures used in quantum information with qubits, arbitrary dimension qudits,
and quantum continuous variables. This \emph{general quantum variables}
construction provides a succinct language for formulating many results in
quantum computation and information so that they are applicable in all
dimensions. The structures included within this formalism include: a
generalization to arbitrary dimension of the three Pauli operators, and the
associated mutually unbiased bases; the Pauli and Clifford groups; many
important quantum gates; standard sets of generators for the Clifford group;
and simple universal gate sets. This formalism provides a convenient, intuitive
and extensible language for easily generalizing results that were originally
derived for a single type of system (often qubits or quantum continuous
variables), and that rely on only those structures listed above, to apply in
all dimensions.
