I assume it's the private key that's under your finger. Without any additional security measures, how can one be sure that a paper coin is unspent?
The idea with these is that the receiver of a bill scans the private key, immediately moving the funds to another address. The bill can then be discarded.
So to scan it you'd need a mobile phone, what's the benefit of having paper at all then? I'm trying to think of uses for this and it seems there's very limited and specific scenarios it'd be useful.