Quantum operation, quantum Fourier transform and semi-definite programming

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Journal Article
Physics Letters, Section A: General, Atomic and Solid State Physics, 2004, 323 (1-2), pp. 48 - 56
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We analyze a class of quantum operations based on a geometrical representation of d-level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier transform, is found for this class of operations. A more general class of operations on qudits is also considered and its completely positive condition is reduced to the well-known semi-definite programming problem. © 2004 Elsevier B.V. All rights reserved.
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