Hypothetically impossible. Routing requires understanding where the packet is to go, combining it with other packets going through the "router" and then sending those along to their destination in an efficient way. To do this inspection of the packets, you have to get information from it in some way. Our understanding of quantum physics doesn't allow this, so trying to inspect the packet in any way will create a false positive that the encryption has been broken. There's no way(again, that we know of) that can tell a false positive from a real positive in this case.
Your question is basically what the entire article is about. Short answer: difficult when dealing with a system that by design is not supposed to read any part of the data.
"The current generation of quantum cryptography systems are point-to-point connections over a single length of fibre, So they can send secure messages from A to B but cannot route this information onwards to C, D, E or F. That’s because the act of routing a message means reading the part of it that indicates where it has to be routed. And this inevitably changes it, at least with conventional routers. This makes a quantum internet impossible with today’s technology"
Impossible with today's technology = extremely difficult.
Routers have to read the data in order to know where it is supposed to be routed to. Quantum routing isn't allowed to do that. That's a difficult problem.
edit: apologies for duplicating previous answers, should've refreshed the comments page before posting.
TFA talks about it a bit, but your biggest problem is multiplexing/demultiplexing, since that requires you to essentially create a MITM attack (i.e. read the data at a 3rd point besides the sender/reciever), which kind of defeats the purpose of quantum computing. They mention a hub based system, but again, TFA talks about scaling which can be very hard to do when you're essentially relying on a single point of failure that has to scale with the entire network.
They talk about the problem with it so far in the article:
"The current generation of quantum cryptography systems are point-to-point connections over a single length of fibre, So they can send secure messages from A to B but cannot route this information onwards to C, D, E or F. That’s because the act of routing a message means reading the part of it that indicates where it has to be routed. And this inevitably changes it, at least with conventional routers. This makes a quantum internet impossible with today’s technology"
So to incorporate routing, we're going to have to get a bit more clever.
Well, the way that immediately comes to mind would be to send two packets per transmission. One that is point-to-point, which contains the routing information, and one that is meant to be routed without being read, but there must be something more to it as this solution seems too simple to have not been thought of.
Well they do mention that they "solved" this problem:
"Today, Richard Hughes and pals at Los Alamos National Labs in New Mexico reveal an alternative quantum internet, which they say they’ve been running for two and half years. Their approach is to create a quantum network based around a hub and spoke-type network. All messages get routed from any point in the network to another via this central hub.
This is not the first time this kind of approach has been tried. The idea is that messages to the hub rely on the usual level of quantum security. However, once at the hub, they are converted to conventional classical bits and then reconverted into quantum bits to be sent on the second leg of their journey."
With a little more reading, it seems like the issue they face now is the reliance on a secure central hub.
