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I was reading about quantum teleportation using Qiskit. Alice wants to teleport some quantum state to Bob. My question is Is it possible for bob just to see the state vector after receiving it from Alice without measuring it?

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No, this is not possible. The state vector describes a distribution of a possible outcomes after measurement the quantum state. So, to reconstruct the state vector, the measurement has to be performed.

If you can assume that the amplitudes in the state vector are real numbers only, you can only repeat the measurement several times in the computational basis to get reasonable statistics.

However, when a quantum phase is involved (i.e. the amplitudes are complex), you have to measure in other bases (e.g. Hadamard)as well or do complete tomography to reconstruct the state vector.

Note that in Qiskit you can employ statevector_simulator which reveals the state vector, however, as the name suggest, it only a simulation on a classical computer. In quatum world, the measurement (even repeated one) is necessary to get the state vector.

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  • $\begingroup$ Thank you for responding, So if my amplitudes are complex numbers then I can use tomography to reconstruct back the complex amplitudes after I measured it? Is that correct? Or did I understand it wrong. $\endgroup$
    – User1086
    Mar 27 at 0:29
  • $\begingroup$ Yes, for general state. For one qubit it is possible to use a method proposed here: quantumcomputing.stackexchange.com/questions/11354/… However, the measurement cannot be avoided. $\endgroup$ Mar 27 at 7:32
  • $\begingroup$ So by that I will teleport the quantum state for Alice to Bob and at Bobs side I have to do tomography to look into state of qubit . $\endgroup$
    – User1086
    Mar 28 at 20:15
  • $\begingroup$ @bhagiradh: Yes, by teleportation you only move the qubits from Alice to Bob. To get whole state vector on Bob side, generally you need to do tomography (with exception to special cases I meant before). $\endgroup$ Mar 29 at 5:50
  • $\begingroup$ There is no 'moving' of qubits involved in teleportation. Moreover, it should be noted you need _many copies _ of a state to perform state tomography - you cannot determine the full state of a single qubit. $\endgroup$
    – JSdJ
    Apr 1 at 8:59

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