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Quantum operation, quantum Fourier transform and semi-definite programming

Runyao Duan·Zhengfeng Ji·Yuan Feng·Mingsheng Ying
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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.

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Runyao Duan, Zhengfeng Ji, Yuan Feng, Mingsheng Ying. 2003-12-25. Quantum operation, quantum Fourier transform and semi-definite programming. https://doi.org/10.1016/j.physleta.2004.01.045

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