Unital quantum operations on the Bloch ball and Bloch region
Paul Bourdon, H. T. Williams · Physical Review A · 2004
For one-qubit systems, we present a short, elementary argument characterizing unital quantum operators in terms of their action on Bloch vectors. We then show how our approach generalizes to multiqubit systems, obtaining inequalities that govern when a ``diagonal'' superoperator on the Bloch region is a quantum operator. These inequalities are the n-qubit analog of the Algoet-Fujiwara conditions. Our work is facilitated by an analysis of operator-sum decompositions in which negative summands are allowed.