No, as you can't influence the outcome of the measurement. So both parties reads a bit, which is random, they just happen to be opposite of eachother. No useful information is transmitted.
I also wonder what is meant here.
Are the particles no longer entangled after they are measured once, or what is being said here?
It is actually quite difficult to keep the particles entangled, because the rest of the universe keeps trying to measure them. (I am not a physicist, and I have no idea how they keep the particles entangled.)
I have a feeling that terms being used are specifically defined terms of art. EG, don't mean what they mean in common english, but instead, have a different technical meaning.
Option 1 is that you read it before the state of A is read, in which case my undestanding is you are effectively A in this scenario.
Option 2 is that the state of A has been read, but it is unkown to you yet, because of speed of light reasons. You read B, and can infer the state of A, but because A is random, no information has been transmitted. The "sender" cannot control which state of A they read, and had you not known about it, the state of B might as well be random.
Option 3 is that you read B after recieving the state of A, in which case there is something useful in that only you can make sure that only the sender knew of the state of A, meaning you are effectively authenticating a message. But still no information has been transmitted faster than light, it's just a secure channel.
If you are looking at A alone, A is random.
If you are looking at B alone, B is random.
If you are looking at A and B together, they are entangled, i.e. their probabilities are "50% chance A head B tails, 50% chance A tails B head".
Random means something you can't predict (other than statistically), until it actually happens. If you know the state of the entire universe except for the particle B, you can't predict A. If you know the state of the entire universe except for the particle A, you can't predict B.