Sensor to check if door is locked
You probably need an Arduino, to check with a sensor if the door is locked or not. You could use a sensor depending on what you kind is best.

The Arduino would receive / process the signal from the sensor (which is probably near/connected to the lock).

Than you need some kind of rF/wifi or other wireless shield or component to send it to the key.

Your key need to be able to receive this, which may need another Arduino. I would not opt for an Uno since these are way too big. Even a Micro can be already big as a 'key' with intelligence.