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

J. Solomon Ivan, Krishna Kumar Sabapathy, R. Simon

Continuous-variable systems in quantum theory can be fully described through any one of the $\mathrm{s}$-ordered family of quasiprobabilities ${\Lambda }_{\mathrm{s}}(\alpha )$, $\mathrm{s}\in [-1,1]$. We…