. We experimentally demonstrate these findings using a single cesium atom confined in an optical dipole trap, which undergoes a nearly pure dephasing process. Our method can be applied straightforwardly to multi-atom systems for measuring the Wigner function of their collective spin state.

DOI: 10.1103/physreva.97.013840

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\frac{2}{3}

\frac{2}{3}

. We experimentally demonstrate these findings using a single cesium atom confined in an optical dipole trap, which undergoes a nearly pure dephasing process.

Gibbons et al., [Phys. Rev. A 70, 062101 (2004)] have recently defined discrete Wigner functions

W

to represent quantum states in a Hilbert space with finite dimension. We show that such a class of Wigner functions

W

can be defined so that the only pure states having non-negative

W

for all such functions are stabilizer states, as conjectured by Galv\~ao, [Phys. Rev. A 71, 042302 (2005)]. We also show that the unitaries preserving non-negativity of

W

for all definitions of

W

in the class form a subgroup of the Clifford group. This means pure states with non-negative

W

and their associated unitary dynamics are classical in the sense of admitting an efficient classical simulation scheme using the stabilizer formalism.