We know that there is something spooky (Einstein) happening since the the quantum state of one entangled particle is immediately "known" by the other so as we can know with certainty the spin of both particles by knowing just one, no matter the distance. Teams in Israel have even entangled particles that didn't exist at the same time.
Regrettably, all we can glean thusly is the spin. The particles themselves cannot transmit or communicate information about their surroundings, nor is there any (known) way to extract any such information.
Still...a very creative approach to thinking about the problem of observing and learning about black holes!