# EPR pair and individual operations [closed]

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?

• 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
– glS
Feb 11 '21 at 11:02
• @glS I will try that. But I am sure this question was concept clearing. But I will do that next time. Feb 11 '21 at 11:14

(1) The best description that I can give is a mixed state, $$\rho=I/2$$.
(3) The combined state looks like $$(|01\rangle+|10\rangle)/\sqrt{2}$$.
• 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? Feb 10 '21 at 14:23
• Ok now I know why it is $I/2$. Thanks. Feb 10 '21 at 15:55
• 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? Feb 10 '21 at 16:01
• 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. Feb 11 '21 at 7:45