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For the $|W_3\rangle=\frac{1}{\sqrt{3}}(|001\rangle+|010\rangle+|100\rangle)$, what does W stand for? Does it refer to an author name? Anyone knows a reference? Thanks

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Apparently $\vert W \rangle$ was first reported (and the naming convention first adopted) by Dür, Vidal and Cirac in this preprint on May 26, 2000 (version 1 of 2).

This is supported by the footnote on page 4 of this preprint on June 25, 2000 (version 3 of 3, this footnote did not appear in the earlier versions), which states (in part)

Very recently Dürr [sic], Vidal, and Cirac (LANL eprint quantph/0005115) have found a tripartite pure state of 3 qubits which is stochastically incomparable with the GHZ state.

Dür, Vidal and Cirac don't explicitly ascribe any special significance to the notational choice $\vert W \rangle$, so it seems that only the authors could say with any confidence whether $W$ has any significance.

Edit: The lead author's first initial is W. (for Wolfgang), which is plausible motivation for the notation $\vert W \rangle$, but I'm not aware of any evidence to support this.

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    $\begingroup$ I, for one, really appreciate the lack of DVC notation - I struggle enough with GHZ, trying to misspell it as GHC or something else about half of the time :-) $\endgroup$ – Mariia Mykhailova Oct 21 at 2:01
  • $\begingroup$ Thanks for the answer. I did search DVC paper and could not find an explanation. I will wait to see if any other information pops up. If not, I will accept your answer. $\endgroup$ – czwang Oct 22 at 0:00
  • $\begingroup$ @MarkS Yeah, it's definitely speculative. Edited to add qualification to edit and link abstracts. $\endgroup$ – ChainedSymmetry Oct 22 at 0:48
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    $\begingroup$ Anecdotally, I was originally told that the three peaks of the letter W stood for the positions of the single '1' in each of the standard basis components. $\endgroup$ – Niel de Beaudrap Oct 23 at 8:40
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    $\begingroup$ @NieldeBeaudrap ha! We could write the $|W\rangle$ state as the $|Ш\rangle$ state! $\endgroup$ – Mark S Oct 29 at 14:54

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