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I have created an EPR pair. Let's suppose it's $(|00\rangle + |11\rangle)/\sqrt{2}$. We both of our halves and then we move into our places.

  1. If I ask you how does your half look like (mathematical expression of the state), what would be the answer? (How does my half look like?)

  2. If I apply some operation to my half like maybe applying pauli $X$ gate which flips qubits, would it change anything in your half?

  3. What would the combined state look like after this operation?

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  • $\begingroup$ please ask a single, laser-focused question per post. You can ask different questions on different posts. Also, the title should reflect what (specifically) is actually been asked in the question $\endgroup$
    – glS ♦
    Feb 11, 2021 at 11:02
  • $\begingroup$ @glS I will try that. But I am sure this question was concept clearing. But I will do that next time. $\endgroup$
    – user27286
    Feb 11, 2021 at 11:14

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(1) The best description that I can give is a mixed state, $\rho=I/2$.

(2) If you apply a unitary operation on your half, it does not change my description of my state. If you apply a measurement on your half, my best description only updates if you tell me the measurement result.

(3) The combined state looks like $(|01\rangle+|10\rangle)/\sqrt{2}$.

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  • $\begingroup$ Now I see your answer. Thanks for answering. I have one question, can you give me an idea of how you arrive at $\rho$? What is the meaning of it? $\endgroup$
    – user27286
    Feb 10, 2021 at 14:23
  • $\begingroup$ Ok now I know why it is $I/2$. Thanks. $\endgroup$
    – user27286
    Feb 10, 2021 at 15:55
  • $\begingroup$ Still I have one more question. We have got the representation of state via density operator. So if I apply X, then how would it change in my case? (Because I don't have anything of the form $\alpha |0\rangle + \beta|1\rangle$? And once I tell you that, how would you state change? Wait a second, I can do anything I want i wont matter unless I measure something and tell you right? $\endgroup$
    – user27286
    Feb 10, 2021 at 16:01
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    $\begingroup$ The description of your qubit is $\rho_A$, the description of my qubit is $\rho_B$. If you do $X$ to your qubit, yours becomes $X\rho_AX$. Mine does not change. $\endgroup$
    – DaftWullie
    Feb 11, 2021 at 7:45

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