1. Nothing. Quantum Key Distribution is what they're talking about, and it still requires P!=NP because there's a classical cryptographic step involved (several, actually). It just allows you to exchange symmetric keys with a party you've used classical cryptography to authenticate, it's vulnerable to MITM attacks otherwise. So you're dependent on classical signatures and PKI to authenticate the endpoints. And you're exchanging classical symmetric keys, so still dependent on the security of classical encryption like AES-GCM.
2. Because they're not 100% secure. Only the key exchange step with an authenticated endpoint is 100% secure.
3. Eavesdropping acts like a denial of service and breaks all communications on the channel.
4. It makes the information useless to everyone, both the eavesdropper and the recipients. Attempting to eavesdrop on a QKD channel randomizes the transmitted data. It's a DOS attack. The easier DOS attack is to break the fiber-optic cable transmitting the light pulses, since every endpoint needs a dedicated fiber to connect to every other endpoint.
> Only the key exchange step with an authenticated endpoint is 100% secure.
It's 100% secure in theory, assuming a model of the hardware (which is impossible to verify even if you could build it to "perfectly" satisfy all model assumptions, which of course you also can't).
2. Because they're not 100% secure. Only the key exchange step with an authenticated endpoint is 100% secure.
3. Eavesdropping acts like a denial of service and breaks all communications on the channel.
4. It makes the information useless to everyone, both the eavesdropper and the recipients. Attempting to eavesdrop on a QKD channel randomizes the transmitted data. It's a DOS attack. The easier DOS attack is to break the fiber-optic cable transmitting the light pulses, since every endpoint needs a dedicated fiber to connect to every other endpoint.