Unital quantum operators on the Bloch ball and Bloch region

Details Unital quantum operators on the Bloch ball and Bloch region Unital quantum operators on the Bloch ball and Bloch region

2003-08-17

arxiv.org/abs/quant-ph/0308089v2

Physics

Quantum Physics

Revised and corrected, to appear in Physical Review A

Scientific paper

10.1103/PhysRevA.69.022314

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 multi-qubit systems, obtaining inequalities that govern when a ``diagonal'' superoperator on the Bloch region is a quantum operator. These inequalities are the n-qubit analogue of the Algoet-Fujiwara conditions. Our work is facilitated by an analysis of operator-sum decompositions in which negative summands are allowed.

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