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Unital quantum operators on the Bloch ball and Bloch region

P. S. Bourdon·H. T. Williams
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Abstract

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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P. S. Bourdon, H. T. Williams. 2003-12-13. Unital quantum operators on the Bloch ball and Bloch region. https://doi.org/10.1103/physreva.69.022314

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