Discrete phase-space mappings, tomographic condition and permutation invariance. (7th March 2017)

• Record Type: Journal Article
• Authors: Muñoz, C; Klimov, A B
• Is Part Of: Journal of physics. Volume 50:Number 14(2017)
• Publication Date: 2017-03-07
• Subjects: phase-space -- discrete -- Wigner function -- symmetric; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa5fb5
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We analyze various families of discrete maps in N -qubit systems in the context of permutation invariance. We prove that the tomographic condition imposed on the self-dual (Wigner) map is incompatible with the requirement of the invariance under particle permutations (except for the two-qubit case), which makes it impossible to project the Wootters-like Wigner function into the space of symmetric measurements. We also provide several explicit forms of the self-dual mappings: (a) tomographic and (b) permutation invariant, and analyze the symmetric projection in the latter case.