There is some confusion regarding QKD. The confusion revolves around the underlying principle and it's nuts & bolts implementation in the physical world. The two are conflated, which I believe is unfair as QKD is an emerging technology so shouldn't be so harshly compared with centuries year old cipher principles.
So in this quantum version, what makes it more secure than the classical version?
QKD per se is unlike sending an electrical signal through a network cable. If the following is a QKDN like so
Eve cannot avoid being noticed. This is the crux and often missed. She cannot eavesdrop without affecting the photon stream between Alice and Bob. This is fundamental to life, the universe and quantum mechanics and is called the Observer Effect.
...why can't Eve intercept this encrypted message and as usual try to figure out the key (which is a string of 0s and 1s) like in classical cryptography?
Eve doesn't have to figure out the message. She can just read it directly from the photon beam. But Alice and Bob will notice. They then either retry the transmission, or send out a ruthless search & destroy team to obliterate Eve. The point here is that no key exchange completes if Eve is listening. There is no such effect in an Ethernet cable. This is why the NSA can secretly tap all our phones, but not the photon stream within a QKDN.
Of course the whole QKD hardware has to operate in the physical world. That makes it susceptible to traditional attacks and compromises. It's important that people do not conflate the Observer Effect underpinning QKD with a server's resistance to a thermite grenade or a computer hacker.
