2006/01/03 by Cecilia Cormick, Ernesto F. Galvão, Daniel Gottesman +3 · 4 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications
paper · doi:10.1103/physreva.73.012301
openalex publication_date 2006/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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.