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I'm reading the paper Implementation of the Quantum Fourier Transform. On page 4, they write

To a first approximation, decoherence during the course of the QFT attenuates the entire density matrix. This is shown in figure 2.

I know that the word "attenuate" means to dampen or reduce the force of something. Since density operators have trace one, perhaps this means that the QFT decreases the trace of the density operator...

My questions are

  1. What is meant by attenuate here?
  2. Why does decoherence during the course of the QFT do this, and why "to a first approximation"?
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    $\begingroup$ I'd guess what is meant is that decoherence decreases the off-diagonal elements of the density matrix. $\endgroup$ – Norbert Schuch Mar 1 at 14:59
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    $\begingroup$ And please link to the abstract rather than the PDF - this is extremely annoying if one is just interested in knowing what paper that is. $\endgroup$ – Norbert Schuch Mar 1 at 15:00

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