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I was reading about quantum compression in this article and have some doubts regarding an example mentioned. Specifically, I have two questions:

  1. In example they represented $|a\rangle = \dfrac{1}{\sqrt{15}}|00\rangle + \dfrac{1}{\sqrt{15}}|10\rangle +\dfrac{2}{\sqrt{15}}|01\rangle + \dfrac{1}{\sqrt{15}}|11\rangle$. How can they call this a quantum state given that the sum of square magnitudes of the amplitudes is not equal to one?
  2. If they are compressing kets ($|10\rangle$ to $|1\rangle $) then what is the point of the amplitudes $\dfrac{1}{\sqrt{15}}$?
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  • $\begingroup$ I'd add that the author says the state $|a\rangle$ is a mixed state. Weird. $\endgroup$
    – kludg
    Apr 19 at 3:34
  • $\begingroup$ can you reformat the question to focus it on a single point? The stackexchange format is tailored for laser-focused posts; feel free to edit the question accordingly. It would also help to make the post self-contained by sketching what exactly is meant in the linked text with "compression". A meaningful title would also help $\endgroup$
    – glS
    Apr 19 at 9:30
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    $\begingroup$ Well, the question 1 is enough to raise doubts that the Journal of Applied Sciences is a meaningful scientific journal. $\endgroup$
    – kludg
    Apr 19 at 13:21
  • $\begingroup$ @kludg The publisher "science alert" is on Beall's list of potential predatory journals/publishers. $\endgroup$
    – Rammus
    Apr 19 at 15:45
  • $\begingroup$ A serious note on the first question though, it is possible the author is just writing the state "up to normalization". So you just have to normalize the given state. Would this make sense in the context of the paper? $\endgroup$
    – Rammus
    Apr 19 at 15:53

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