I'm building a world for a role-playing game campaign using the Stars Without Number system.
Some background information first:
Stars Without Number Original Setting: In the original story provided by the SWN book, humanity has reached a post-scarcity level of technology and has traveled and settled to other star systems using (a) FTL travel, and (b) worm-hole-like portals. However, at some point, a cosmic event happened called The Scream which destroyed the portals and drove many people mad across the universe, effectively cutting out colonies from one another. As a result most planets were set back centuries both from a technological and a social/cultural perspective.
Quantum Entanglement Communication: In the Mass Effect series there is a type of communication based on quantum entanglement. The upside of QEC is that it allows two ends to communicate instantly no matter the distance. The downside is that, the way quantum entanglement works, you can only create a communication channel between points A and B, as opposed to other ways of communicating where you can broadcast your message to several/countless endpoints.
In my setting FTL travel is being discovered and humanity starts settling on hundreds of nearby systems. There are no wormhole-like portals, the only way to get to a star is via FTL travel.
As it happens every time a powerful nation establishes colonies, Earth attempted to maintain control. The way Earth did that was via setting up QEC systems between itself and most of the planets and acted as central hub of communication for everyone, similarly to how telephone centers used to operate. Remember, the downside of QEC is that it establishes communication only for points A and B. This means that if Colony B wants to send a message to Colony C they will have to go through Earth (Point A).
However, at some point, Earth was overtaken by unbraked/sentient AIs and this communication hub was destroyed leading the colonies to panic and chaos.
Earth would want to keep QEC technology a secret. Otherwise, some of the colonies may establish QEC systems between themselves. If you attempt to keep the technology secret from a single colony you can guard it using a substantial force. But that becomes increasingly difficult when the colonies number in the order of hundreds. So, how is it possible that Earth kept the how-to of this technology a secret for a long time on so many different worlds?
p.s. There is a similar question however the answers specifically address the scenario described by the OP and thus they are not suitable for my setting.