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• W3113052783 startingPage "4023" @default.
• W3113052783 abstract "Motivated by quantum thermodynamics we first investigate the notion of strict positivity, that is, linear maps which map positive definite states to something positive definite again. We show that strict positivity is decided by the action on any full-rank state, and that the image of non-strictly positive maps lives inside a lower-dimensional subalgebra. This implies that the distance of such maps to the identity channel is lower bounded by one. The notion of strict positivity comes in handy when generalizing the majorization ordering on real vectors with respect to a positive vector $d$ to majorization on square matrices with respect to a positive definite matrix $D$. For the two-dimensional case we give a characterization of this ordering via finitely many trace norm inequalities and, moreover, investigate some of its order properties. In particular it admits a unique minimal and a maximal element. The latter is unique as well if and only if minimal eigenvalue of $D$ has multiplicity one." @default.
• W3113052783 created "2020-12-21" @default.
• W3113052783 creator A5062883307 @default.
• W3113052783 date "2020-12-17" @default.
• W3113052783 modified "2023-10-16" @default.
• W3113052783 title "Strict positivity and <i>D</i>-majorization" @default.
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• W3113052783 doi "https://doi.org/10.1080/03081087.2020.1860887" @default.
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