Quantum operations fixing a convex cone of density operators on T(H)

The unital quantum operation acting on infinite dimensional quantum states fixing a convex cone of density operators is completely characterized. Based on this result, we classify the commutativity of two quantum operations and determine what kind of measurement statistics are preserved by a unital quantum operation. Our work extends the results of Lee et al (2013 J. Phys. A: Math. Theor. 46 205305) to the infinite dimensional case and also corrects part (a) of theorem 6 in Lee et al (2013 J. Phys. A: Math. Theor. 46 205305). (paper)