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The paper, Quantum deletion is possible via a partial randomization procedure claims that it is possible to bypass the no-deleting theorem by a procedure called R-deletion. But this seems to go against the original no-deleting theorem. If not, why so?

And doesn't the following line from the first paper actually convey a swapping operation which has been categorically excluded by Pati and Braunstein?

But, whatever this state be in our actual realization of R-deletion, we do not recover now, from the linearity of Quantum Mechanics, the result in {1} that $|A_\psi\rangle= \alpha|A_H\rangle +\beta|A_V\rangle$.

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