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Classicality in discrete Wigner functions
Cecilia Cormick, Ernesto F. Galvao, Daniel Gottesman, Juan Pablo Paz, Arthur O. Pittenger
abstract: Gibbons et al. [Phys. Rev. A 70, 062101(2004)] have recently defined a class
of discrete Wigner functions W to represent quantum states in a Hilbert space
with finite dimension. We show that the only pure states having non-negative W
for all such functions are stabilizer states, as conjectured by one of us
[Phys. Rev. A 71, 042302 (2005)]. We also show that the unitaries preserving
non-negativity of W for all definitions of W 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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0506222
- categories:
- quant-ph
- comments:
- 10 pages, 1 figure
- doi:
- 10.1103/PhysRevA.73.012301
- arxiv_id:
- quant-ph/0506222
- journal_ref:
- Phys. Rev. A 73, 012301 (2006)
- created:
- 2005-06-27
Full article ▸
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