Discrete phase-space mappings, tomographic condition and permutation invariance
arXiv:1603.00916 · doi:10.1088/1751-8121/aa5fb5
Abstract
We analyze different families of discrete maps\ in the N-qubit systems in the context of the 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, which makes it impossible to project the Wootters-like Wigner function into the space of symmetric measurements. We also provide several \textit{explicit} forms of the self-dual mappings: a) tomographic and b) permutation invariant \ and analyze the symmetric projection in the latter case.
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