The question is as stated in the title, very simple. I just need a definite answer on this since I am working with a diagrammatic method of quantum mechanics where this fact might come in very handy.

Maybe I should take this to the math stackexchange?


closed as unclear what you're asking by G. Smith, Thomas Fritsch, Kyle Kanos, Jon Custer, ZeroTheHero Sep 11 at 21:19

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    $\begingroup$ You need to define what you mean by “positive map”. If there are two outputs, it isn’t obvious what “positive” means. $\endgroup$ – G. Smith Sep 10 at 19:15
  • $\begingroup$ @G.Smith why should the number of inputs or outputs matter here? A positive map is a map $\mathcal E$ such that $\mathcal E(\rho)\ge0$ for all states $\rho$ (see e.g. here). Or is the OP referring to some other definition? $\endgroup$ – glS Sep 11 at 9:33