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For example, has anyone seen something like:
"quqrit" for a 4-level system[1], or
"qupit" for a 5-level system[2] ?

1 From "quad" or "quart" since "tetra" would be qutrit, which is already a 3-level system.
2 From "penta" since "quint" would interfere with quqrit for 4-level system.

I understand that we could call a quqrit a "spin-3/2 particle" which would be overloading the meaning of spin, but I wonder if these terms have ever been used. I have searched "quqrit" and "qupit" on Google but what if it's not called "quqrit" but something else? Also, perhaps no one had the bravery to publish something with these words written down but have been used orally at conferences. Surprisingly, after asking this question I found one paper using the term "qupit" but the word only appears in the title and nowhere else, so it's not clear what their definition of qupit is!

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  • $\begingroup$ That's mixing up when to choose Greek prefix and when to use Latin. If you really want to do it that way, fine. $\endgroup$ – AHusain May 19 '18 at 2:18
  • $\begingroup$ Yes I explained why I mixed Greek and Latin. It's not the first time it's been done: automobile is from autos = Greek for self, and mobilis = Latin for movement. $\endgroup$ – user1271772 May 19 '18 at 3:05
  • $\begingroup$ If not quqrit, then ququit, or quqit ? $\endgroup$ – user1271772 May 19 '18 at 4:35
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There is no standard name for a qudit for $d>3$. The community has mostly settled on the term qudit (but you will still find qunit or quNit, for example, using $n$ or $N$ instead of $d$ in some older papers).

You will find the odd paper where an individual author will pick a name for the $d=4$ case. I’ve certainly seen ququad and ququart. But I think mostly people just use qudit, and specify $d$.

The other term that you'll see (thanks to Niel de Beaudrap for pointing it out) is qupit, a quantum system where the Hilbert space dimension is an odd prime, $p$.

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  • $\begingroup$ I think that "qupit" is a newer term, and is meant specifically to refer to a qudit of odd prime dimension (since this is the case for which the number theory associated with the stabiliser formalism is the least awkward). $\endgroup$ – Niel de Beaudrap May 20 '18 at 9:29
  • $\begingroup$ @NieldeBeaudrap Good point! I suspect I was actually thinking of qunit. Let me rewrite... $\endgroup$ – DaftWullie May 21 '18 at 6:44
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After a lot of searching, it appears that the word "quqrit" has indeed been used in one (but I found only one!) paper from 2011, and indeed it was used to describe a 4-level system. But the word "quqit" is used to describe 4-level systems in two papers [1][2] dating back to 2004. This time there's four different authors in total, but two of them are on both papers so no independent groups using this term (as far as I have found).

As for higher-order qudits beyond $d=5$, it appears to be an open question.

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