If and when we upload a mind to a computer and/or create true AI, this question will be settled for all practical purposes.
Why? Because the person in the computer, being a faithful simulation of a human mind (or some AI analogue), will say they feel exactly the same mental things as real humans, down to the most minor detail. You then see they are just software, and say it's impossible to prove they feel the subjective experience they claim to feel.
Then they say you're just a dude and it's impossible for you to prove you feel this subjective experience you claim to feel.
There's no way out. If it's possible _at all_ to have self-aware software, they will have exactly the same claim to consciousness as yourself. Which is: I can't show my mental state to anyone and you need to take my word for granted.