A problem relating to positive linear maps on matrix algebras
This paper deals with a problem which is solved in the commutative case but still unknown in the matrix cases. Namely, let X, Y, Z, Z' be density matrices. Does there exist a stochastic map (i.e. a linear, positivity- and trace-preserving one), say, L, such that \(X=L(Z)\), \(Y=L(Z')\), in the case that \(\| X-tY\|_ 1\leq \| Z-tZ'\|\), for all positive numbers t. The authors are able to find an affirmative answer in the 2\(\times 2\)-case.
scientific article; zbMATH DE number 3847582