Classicality in discrete Wigner functions

Journal Article · Sun Jan 15 04:00:00 EST 2006 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.73.0· OSTI ID:20786646

Cormick, Cecilia ^[1]; Galvao, Ernesto F; Gottesman, Daniel ^[2]; Paz, Juan Pablo ^[1]; Pittenger, Arthur O ^[3]

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1. Departamento de Fisica 'Juan Jose Giambiagi', FCEyN UBA, Pabellon 1, Ciudad Universitaria, 1428 Buenos Aires (Argentina)
2. Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, N2L 2Y5 (Canada)
3. Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, Maryland 21250 (United States)

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 Galvao, [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.

• OSTI ID: 20786646
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 73; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ENERGY LEVELS
FUNCTIONS
HILBERT SPACE
QUANTUM COMPUTERS
SIMULATION
WIGNER DISTRIBUTION