If this escalates outside of diplomatic talks ...
The key is in the satellites and their encryption.
Whoever controls the strongest network of communication satellites wins [unless their signals are scrambled].
China gained access to our encryption, and the NSA got hacked.
Ping.
Everybody has access to the same encryption algorithms. If we did not, then we would have security by obscurity which always fails eventually. What China could conceivably do is crack our encryption keys using quantum computing. AFAIK that hasn't been done yet, but I'm sure they and the NSA are working on it. Also, as you mentioned, they could protect their own comms using quantum encoding of some sort. I don't know that works at line speeds yet. It works in the lab but AFAIK only at low speeds.
Whoever controls the strongest network of communication satellites
We have are uniquely vulnerable in space comms mainly by having the most to lose. I don't think an attack on encryption is the worst threat. The worst threat is destroying or disabling our satellites.