Classicality in discrete Wigner functions
Gibbons, [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 a...
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todo:paper_10502947_v73_n1_p_Cormick2023-10-03T15:59:46Z Classicality in discrete Wigner functions Cormick, C. Galvão, E.F. Gottesman, D. Paz, J.P. Pittenger, A.O. Computer simulation Quantum theory Discrete Wigner functions Hilbert space Unitary dynamics Functions Gibbons, [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. © 2006 The American Physical Society. Fil:Cormick, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Paz, J.P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10502947_v73_n1_p_Cormick |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Computer simulation Quantum theory Discrete Wigner functions Hilbert space Unitary dynamics Functions |
| spellingShingle |
Computer simulation Quantum theory Discrete Wigner functions Hilbert space Unitary dynamics Functions Cormick, C. Galvão, E.F. Gottesman, D. Paz, J.P. Pittenger, A.O. Classicality in discrete Wigner functions |
| topic_facet |
Computer simulation Quantum theory Discrete Wigner functions Hilbert space Unitary dynamics Functions |
| description |
Gibbons, [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. © 2006 The American Physical Society. |
| format |
JOUR |
| author |
Cormick, C. Galvão, E.F. Gottesman, D. Paz, J.P. Pittenger, A.O. |
| author_facet |
Cormick, C. Galvão, E.F. Gottesman, D. Paz, J.P. Pittenger, A.O. |
| author_sort |
Cormick, C. |
| title |
Classicality in discrete Wigner functions |
| title_short |
Classicality in discrete Wigner functions |
| title_full |
Classicality in discrete Wigner functions |
| title_fullStr |
Classicality in discrete Wigner functions |
| title_full_unstemmed |
Classicality in discrete Wigner functions |
| title_sort |
classicality in discrete wigner functions |
| url |
http://hdl.handle.net/20.500.12110/paper_10502947_v73_n1_p_Cormick |
| work_keys_str_mv |
AT cormickc classicalityindiscretewignerfunctions AT galvaoef classicalityindiscretewignerfunctions AT gottesmand classicalityindiscretewignerfunctions AT pazjp classicalityindiscretewignerfunctions AT pittengerao classicalityindiscretewignerfunctions |
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1807315410497830912 |