Let A has quantum memories $M_1$ and $M_2$ and B has quantum memories $M_3$ and $M_4$ capable of holding one qubit.

2 Bell states are shared among A & B in the following way:

First Bell state $|B_{00}\rangle$ has been shared among $M_1$ and $M_3$. Second Bell state $|B_{00}\rangle $ has been shared among $M_2$ and $M_4$.

Assume all calculations are in Bell basis.

How to calculate the Bell states of A[$M_1$ and $M_2$] and B[$M_3$ and $M_4$]?

  • $\begingroup$ Why people are downvoting the question? Whats wrong in the question? $\endgroup$ Sep 28 '19 at 14:45
  • $\begingroup$ Please start using proper LaTeX formatting in your questions. $\endgroup$ Sep 29 '19 at 9:33

Simply start by writing out everything $$ |B_{00}\rangle_{13}|B_{00}\rangle_{24}=\frac12\left(|00\rangle_{13}|00\rangle_{24}+|00\rangle|11\rangle+|11\rangle|00\rangle+|11\rangle|11\rangle\right) $$ Let me rearrange each of these terms $$ \frac12\left(|00\rangle_{12}|00\rangle_{34}+|01\rangle|01\rangle+|10\rangle|10\rangle+|11\rangle|11\rangle\right). $$ Now you can use the fact that the Bell states form a basis to rewrite each of those terms, although maybe it helps to notice that $$ |00\rangle_{12}|00\rangle_{34}+|11\rangle|11\rangle=|B_{00}\rangle|B_{00}\rangle+|B_{01}\rangle|B_{01}\rangle $$ Hence, we get a final answer of $$ \frac12\left(|B_{00}\rangle|B_{00}\rangle+|B_{01}\rangle|B_{01}\rangle+|B_{10}\rangle|B_{10}\rangle+|B_{11}\rangle|B_{11}\rangle\right) $$


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