Transferring GHZ state onto some qubits

This question is just my effort that I made by understanding the previous answers to my questions . I have a GHZ state $$|000\rangle+|111\rangle$$ (please ignore the normalizing constant). For teleportaion of these three qubits (GHZ state) I make use of a 8 qubit cluster channel. I do this in the following way

Can this be the extension of the case when we teleport a Bell state (two-qubit) using 4 qubits cluster state?

Can somebody just check on this circuit? What should be the outcome? Can anybody suggest a possible reference to read?

1 Answer

About checking. I do not quite understand why you can't check how the GHZ-state was teleported in the most ordinary ways: in addition to measuring the state immediately after teleportation, as well as by YYX, YXY, XYY, XXX measurements, you can inverse your GHZ-state and make sure that all 0 are obtained, e.g. like as for this with the most usual GHZ-state teleportation scheme: I think that all listed checking methods (slightly customized) will work with other GHZ-state teleportation schemes, and in addition, the checking method by inversion will work with other desired states (of course, if you can comparing that was before creating state and that became after inversing of state).

About teleportation schemes of arbitrary qubit states via clusters states can see e.g. here.

• I didn't understand your answer. How is your circuit relate to mine Jun 27, 2020 at 9:30
• Sorry, I thought you wanted to know how to check if the GHZ-state was correctly transffered using any circuit, including your circuit. Jun 27, 2020 at 15:39
• Yes i wanted to know does my circut correctly transfer the GHZ state $|000\rangle+|111\rangle$ onto the last three qubits? Jun 27, 2020 at 18:08
• If you know exactly where the part for creating the GHZ-state is located on the circuit (I can assume this part is h(0);cx(0,1);cx(1,2) at top left conner on your circuit), you can check the transferred state by applying an inversion of this part only for last 3 qubits (I can assume it will be cx(9,10);cx(8,9);h(8) for your circuit) before measuring them, make sure that all 3 are equal to 0. This will most likely show that the your circuit correctly transferred your (or other desired) state. You can customize and apply other checks around, but specific to GHZ (see my answer above). Jun 28, 2020 at 9:05
• Okay, so for the state $|000\rangle+|111\rangle$ i should get $50\%$ probability for both the states $000$ and $111$. But, i am not getting this. Is there some procedure whereby you can transfer the states onto some other qubits using cluster state? Jun 28, 2020 at 11:38