In both cases ("Devlet-i ʿAlīye-i" in Ottoman Turkish, and "Dowlat-e Aliyye-ye" in Persian, which are similar in both languages since they derive from Arabic), "sublime state" can be translated as "empire".

Literally, it means "high state". Here, "high" has a range of possible meanings, including the straightforward meaning of "having high elevation", and the metaphorical meanings of "noble", "honoured", etc. "Sublime" and "exalted" are both valid English translations of this "high".

Today, "sublime" and "exalted" have largely lost their original meanings of "having high elevation", and are generally used in their metaphorical sense. Since this is the sense in which "high" in "high state" is used, they are still appropriate translations.

Modern Persian and Modern Turkish will usually use "šâhanšâhi" (Persian, "ruled by the king of kings") or "emperâturi" (Persian) and "imparatorluk" (Turkish), with both of the latter derived from Latin "imperātor".