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Scaling maps of s -ordered quasiprobabilities are either nonpositive or completely positive

par Ivan, Solomon J.S.;Sabapathy, Krishnakumar ;Simon, Richard
Référence Physical Review A, 96, 2, 022114
Publication Publié, 2017-08

Article révisé par les pairs

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Résumé :

Continuous-variable systems in quantum theory can be fully described through any one of the s-ordered family of quasiprobabilities Λs(α), s[-1,1]. We ask for what values of (s,a) is the scaling map Λs(α)→a-2Λs(a-1α) a positive map? Our analysis based on a duality we establish settles this issue: (i) the scaling map generically fails to be positive, showing that there is no useful entanglement witness of the scaling type beyond the transpose map, and (ii) in the two particular cases (s=1,