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Phys. Rev. A 69, 022314 (2004) [7 pages]

Unital quantum operations on the Bloch ball and Bloch region

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P. S. Bourdon*
Department of Mathematics, Washington and Lee University, Lexington, Virginia 24450, USA

H. T. Williams†
Department of Physics and Engineering, Washington and Lee University, Lexington, Virginia 24450, USA

Received 16 August 2003; published 23 February 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.

© 2004 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.69.022314
DOI:
10.1103/PhysRevA.69.022314
PACS:
03.67.Hk, 03.67.Mn, 02.30.Tb

*Electronic address: pbourdon@wlu.edu

†Electronic address: williamsh@wlu.edu

 
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