Classicality in discrete Wigner functions

C. CORMICK; E. GALVAO; D. GOTTESMAN; J. P. PAZ; A. PITTENGER

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

Año: 2006 vol. 73 p. 1 - 9

1050-2947

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 Galvão, [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.