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Suppose Alice has the following state $|\Psi\rangle = \frac{1}{\sqrt2} (|10\rangle + |11\rangle)$

If Alice transfers 1st qubit to Bob then is this the resultant composite system state after transfer?

$\frac{1}{\sqrt2} (|01\rangle + |11\rangle)$

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    $\begingroup$ Hi, I'm not entirely sure what you're asking here - What state did Bob have before Alice transferred her qubit/what was the state of Alice and Bob's combined system? How did Alice 'transfer' her qubit? By 'composite system' do you mean the combined system of Alice and Bob, or something else? $\endgroup$ – Mithrandir24601 Sep 4 at 7:06
  • $\begingroup$ @Mithrandir24601 By composite system I mean the combined system of Alice and Bob. Before the transfer Bob has nothing. I am correcting the question now. $\endgroup$ – Chaitanya Reddy Sep 4 at 7:18
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It seems like you are saying that when Alice sends/teleports her qubit to Bob, the first (left) qubit "becomes" the second (right) qubit. It's like you want to relabel the left (Bob) qubit with the right (Alice) qubit.

However, the states that Alice and Bob have are already a product state and the qubits are not entangled.

For example, Alice's first (left) qubit is not in superposition - it is in the state $|1\rangle$, and her second qubit is superposition in the state $\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)$.

If she sends her first (left) qubit to Bob, then Bob has a qubit in the state $|1\rangle$ while Alice maintains the right qubit in superposition $\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)$.

The net is that up to the relabeling, the resulting qubit system is still $\frac{1}{\sqrt{2}}(|10\rangle+|11\rangle)$.

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  • $\begingroup$ After the teleportation Bob's qubit will be the right qubit of final combined state? As per your answer it is on the left side.. $\endgroup$ – Chaitanya Reddy Sep 4 at 13:43
  • $\begingroup$ It feels like you are contending that teleportation involves some sort of relabeling of indices. It's like you are saying initially the first index (left) is "Alice" and the second index (right) is "Bob," and that after teleportation the first index becomes "Bob" and the second index becomes "Alice." But I don't think that's a standard way to think about things. I think of it more as qubits are these physical but uncompiable units of information that can teleport and move around in space-time, while Alice and Bob are merely positions in space-time. $\endgroup$ – Mark S Sep 4 at 13:59
  • $\begingroup$ I was going through a paper of MPC - Summation Reference: nature.com/articles/srep19655 Please go through step #5 of Page #3.. Player2 passes on the ancillary state of p1 to p3 and the location of ancillary state remains at the same position and p3 is executing unitary operation on ancillary state at the same position and x3 even though secret x2 is in between them. Please clarify. Sadly I am alone trying to learn quantum computing please help me! Instead of discussing this actual problem of mine.. I want to express things in a simple way to clarify the concept.. $\endgroup$ – Chaitanya Reddy Sep 4 at 15:13
  • $\begingroup$ Your question is as if Alice tensored with Bob have two qubits that they pass among themselves. One qubit is not in a superposition, and one qubit is. Do you agree that, in your question, the qubits in Alice's $|\Psi\rangle$ are not entangled? $\endgroup$ – Mark S Sep 4 at 15:28
  • $\begingroup$ In my question state is seperable/not entangled...I got your explanation, But what if the state is entangled? Does positions matter? $\endgroup$ – Chaitanya Reddy Sep 4 at 16:25

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