When you say value of 'state' variable, do you mean the value of "loginClicked" in this sample:
MobileCore.trackAction("loginClicked", additionalContextData);
Basically the Mobile App version of "custom link" value?
You can get this in processing rules using the "a.action" item, unfortunately, Adobe always adds the "AMACTION:" prefix to the action names, but I think that this happens after processing rules, so you should be able to get the value as sent into your dimension.
You can use it in conditions as well: