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Promary Inversion by Catherine Asaro (BOTM 4/2013)
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Quantum entanglement cannot be used to transmit information. Suppose you produce two entangled photons, A and B, say. Quantum entanglement says that if you measure the state of A, then measuring B will give a predictable result, even if the second measurement take place just a moment later but light-years away. This does not allow you to transmit information from A to B, though, because you cannot control the result of either measurement.
Physicists are working on entanglement communication. However, they're finding you can't send meaningful information using ONLY entangled particles A and B. They can use a third particle in a manner which requires sending info about the third particle via non-entanglement communications (which means not FTL). So, you're right the telepathy can't be entanglement without a second means of communication. That could be useful in that the entanglement part of the process can't be easedropped on. Clearly, this isn't what Asaro described.
At hardsf.org, I've written that there's no scientific reason why it might not be possible to have brain implant devices that would act as radio transceivers - permitting a tech-based "telepathy". Although there are reasons to believe it's unlikely alien lifeforms might evolve a radio transceiver organ in their bodies, it should not be considered impossible. There's no reason to believe humans now possess any organs that even represent the first evolutionary steps toward such an organ. However, Primary Inversion takes place thousands of years in the future and there are some references to genetic engineering in this area. So, it would be wrong to simply begin saying this is impossible.
In Primary Inversion, we're told the telepathy works on a quantum basis. The word "entanglement" is not used. However, what other quantum means would there be to send such messages? There's no suggestion of something like a particle beam and receiver. And we're told the ability has to do with two microscopic organs in the brain - which begs the question how a particle beam or such would get out of one head and into another. (Particles like neutrinos could easily pass through a skull, but would usually pass through everything else as well.
Quantum entanglement requires particles to have a previous relationship before one can affect the other. That means each telepath must have a particle with a previous relationship with a particle in the head of anyone he wants to communicate with. In theory, you could have 1000 particle each entangled with each other so each of 1000 telepaths could communicate with any of the other 999. In practice this means whenever any of the 1000 telepaths activates his particle it affects the particle in all the other 999 telepaths. You can never have telepath A talking to B, and at the same time have C talking to D without it getting jumbled up. And that assumes the particle in each telepath's head is never affected by anything other than a telepath's conscious effort to communicate with someone else. The alternative is that each of the 1000 telepaths has to have 999 particles - each entangled with one specific other telepath - and be able to just think who he wants to communicate with and have only that particular particle be activated.
We're also told one telepath can read another telepath's mind unless the other telepath makes an effort to block it. This seems to require one of a few possibilities. First, it could be that a telepath can read a mind that isn't transmitting. Whether we imagine Asaro meant something more like particle beams or quantum entanglement, it doesn't seem to provide a means to receive what wasn't transmitted. Second, we could assume a telepath is always transmitting [except when choosing not to] in some form that any other telepath can receive. This doesn't seem to be consistent with a particle beam (which should be aimed at the recipient). It seems to need transmission via a wave / field or via the "spooky" connection of entanglement. Entanglement has no distance limitation, so if telepaths were always transmitting to everyone [except when trying not to] then every telepath should be constantly receiving from every other telepath. (This is not depicted in the book.) Third, what seems more consistent with the end result is telepaths only transmitting when they choose to and to who they want to. However, that's inconsistent with statements in the book that Telepath A is "blocking" Telepath B from reading A's mind (rather than saying Telepath A is choosing not to transmit to Telepath B.)
I was also skeptical that a microscopic organ which was genetically engineered [biological limited to the possibilities of human cells] would have the energy to and means to operate a quantum system - and while doing so not leak energies or other byproducts which would be harmful to surrounding tissues.