  We introduce a Hermitian generalization of Pauli matrices to higher
dimensions which is based on Heisenberg-Weyl operators. The complete set of
Heisenberg-Weyl observables allows us to identify a real-valued Bloch vector
for an arbitrary density operator in discrete phase space, with a smooth
transition to infinite dimensions. Furthermore, we derive bounds on the sum of
expectation values of any set of anti-commuting observables. Such bounds can be
used in entanglement detection and we show that Heisenberg-Weyl observables
provide a first non-trivial example beyond the dichotomic case.
