Which detect photon's one at a time (also there is spitting out of photons via lasers) The idea is that you have an infallible alarm for when the optics have been tapped, which means that you can then send lots of symmetric keys and know that they can't be intercepted (provided you are only sending them ~50km. So it's nothing to do with cryptography (really) either - which explains why cryptographers aren't that interested in it.
Also it's not a fugazzi as there are several working testbeds in the wild.
What it does is let you expand your pre-existing shared keys in a provably secure manner. And it might be easy if you use satellites, like the Chinese are doing.
"Provable security" is both rare and unnecessary in most of cryptography (in the information theoretic sense relevant to this discussion, not the sense of e.g. application security or static analysis). To reiterate: you do not need information theoretic security to defend against satcom intrusions. That's tantamount to using a one time pad, which is ridiculously inefficient. The computational model is just fine. Even the United States government only rarely uses information theoretic security these days, and instead opts for the more efficient computational security provided by e.g. AES.
No. Quantum key distribution is a fugazzi. It's the red headed step child of actual cryptographic research in the quantum setting. Using quantum key distribution as the basis for a PKI would be ridiculously brittle and over-engineered. Note that the vast majority of interest and research on it comes not from cryptographers, but from physicists who are seeking a cryptographic problem to solve.
It's like saying we should abandon the computational complexity theoretic model of cryptography and go back to the information theoretic model. Basically, it's fairy dust sprinkled onto a one time pad. In modern cryptography the one time pad is (approximately) never used because pseudorandomness is sufficient. Key distribution is not a problem which requires quantum computers to solve. Orchestrating a key distribution ceremony using computers that must extraordinarily well calibrated and synchronized using quantum entanglement would be inefficient and asinine, to put it bluntly.