Quantum operation, quantum Fourier transform and semi-definite programming
arXiv:quant-ph/0304145 · doi:10.1016/j.physleta.2004.01.045
Abstract
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.
16 pages