dorsal/arxiv
View SchemaClassicality in discrete Wigner functions
| Authors | Cecilia Cormick, Ernesto F. Galvao, Daniel Gottesman, Juan Pablo Paz, Arthur O. Pittenger |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0506222 |
| URL | https://arxiv.org/abs/quant-ph/0506222 |
| DOI | 10.1103/PhysRevA.73.012301 |
| Journal | Phys. Rev. A 73, 012301 (2006) |
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.
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"abstract": "Gibbons et al. [Phys. Rev. A 70, 062101(2004)] have recently defined a class\nof discrete Wigner functions W to represent quantum states in a Hilbert space\nwith finite dimension. We show that the only pure states having non-negative W\nfor all such functions are stabilizer states, as conjectured by one of us\n[Phys. Rev. A 71, 042302 (2005)]. We also show that the unitaries preserving\nnon-negativity of W for all definitions of W form a subgroup of the Clifford\ngroup. This means pure states with non-negative W and their associated unitary\ndynamics are classical in the sense of admitting an efficient classical\nsimulation scheme using the stabilizer formalism.",
"arxiv_id": "quant-ph/0506222",
"authors": [
"Cecilia Cormick",
"Ernesto F. Galvao",
"Daniel Gottesman",
"Juan Pablo Paz",
"Arthur O. Pittenger"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.73.012301",
"journal_ref": "Phys. Rev. A 73, 012301 (2006)",
"title": "Classicality in discrete Wigner functions",
"url": "https://arxiv.org/abs/quant-ph/0506222"
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