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Let particle B and C be entangled, created by the EPR source, my understanding is, they are created with certain known superposition state, like this |ψ

_{BC}>=√1/2 (|0

_{A}>|1

_{B}>+|1

_{A}>|0

_{B}>) which in this case, A can be 0 or 1 while B is 1 or 0, can be other possibilities, such as A=1 B=1 or A=0 B=0, but this state is known as the entangle pair is created.

And particle A is another particle. As Alice holds A and B, she will perform a Bell state measurement on A and B to project them into certain Bell state (similar to the one B and C has, four possibilities of the outcome), assume this measured Bell state is orthogonal on A and B, like B and C, then we know A must have the same state as C, since B and C are orthogonal, which the receiver of particle C will gain the state of A.

Please correct me if there is any mistake in my understanding.

Here is the part I failed to understand

1:The entangled known state between B and C will remain as the BSM performed on A and B, is this right?

2: It says that in the entire process, Alice will not know the state of A, is it assumed that Alice doesn't know the entangled state between B and C? If she knows, after the BSM, Alice should be able to know the state of A, is this right?

And I assume this is the reason that extra classical information about the measurement is required from Alice to Bob?

Thanks a lot