At the moment it is not possible, but it would be nice if it will be possible to create an 1:1 relationship between the tables in Dataverse.
There is not a native 1:1 but you can mimic it by putting a Lookup on each entity (for the other end of the relationship) and when you populate one, you also populate the parent using workflow/plugin/flow (and you also stop the creation on another child record if the parent is already populated).
The workaround is to have two relationships, 1-N and N-1 between the two entities and have custom logic (such as classic workflows) to populate the the lookups on each entity. Feel free to vote on this feature request at: https://powerusers.microsoft.com/t5/Power-Apps-Ideas/One-to-one-1-1-relationship-type-in-Common-Data...
And what is the reason why this is not possible atm?
This is because you can already model it by just another Column on the Table. Usually having two Tables with 1:1 is not needed in Dataverse.
It also may be possible to produce this functionality right now, in pretty solid way by using a Custom C# Plugin as well, also alluded to by @Fubar - however, this is also requiring pretty much same setup as the one @EricRegnier suggested with mirroring the N:1 and 1:N with Lookup on both ends, and setting these, and then not setting it if already populated, and if it already can be done with Classic Workflows, that is much simpler to implement than C# plugin, so that is why we recommend you try that suggestion actually if it will accomplish the goal in your case.
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