  It has recently been shown that it is possible to represent the complete
quantum state of any system as a phase-space quasi-probability distribution
(Wigner function) [Phys Rev Lett 117, 180401]. Such functions take the form of
expectation values of an observable that has a direct analogy to displaced
parity operators. In this work we give a procedure for the measurement of the
Wigner function that should be applicable to any quantum system. We have
applied our procedure to IBM's Quantum Experience five-qubit quantum processor
to demonstrate that we can measure and generate the Wigner functions of two
different Bell states as well as the five-qubit Greenberger-Horne-Zeilinger
(GHZ) state. As Wigner functions for spin systems are not unique, we define,
compare, and contrast two distinct examples. We show how using these Wigner
functions leads to an optimal method for quantum state analysis especially in
the situation where specific characteristic features are of particular interest
(such as for spin Schr\"odinger cat states). Furthermore we show that this
analysis leads to straightforward, and potentially very efficient, entanglement
test and state characterisation methods.
