Girl in a state? Quite the reverse! (7)

I believe the answer is:

indiana

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'girl' is the definition.
Although both the answer and definition are singular nouns, I don't understand how they can define each other.

'in a state? quite the reverse' is the wordplay.
'a' becomes 'an'.
'state? quite' becomes 'aid' (I can't justify this - if you can you should believe this answer much more).
'the reverse' says the letters should be written in reverse.
'an'+'aid'='anaid'
'anaid' back-to-front is 'diana'.
'in'+'diana'='INDIANA'

Can you help me to learn more?

(Other definitions for indiana that I've seen before include "Midwestern state" , "State between Illinois/Ohio" , "___ Jones (Raiders of the Lost Ark)" , "Character associated with the Temple of Doom" , "Part of US" .)

I've seen this clue in the Evening Standard.

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