How to get the relative phase of an entangled pair of qubits

Question

I have an extension to the following question: How to get the relative phase of a qubit? How do I get the relative phase of a pair of entangled qubits such as $$\frac{1}{\sqrt{2}}(|00\rangle+e^{i\theta}|11\rangle)$$

in which I want to find theta. I tried to use a similar methodology as the answer in the linked question above, but with no success.

In the thread that was mentioned in the question, there was a mistake in this answer, that is corrected now. — Davit Khachatryan, Jul 27 '20 at 11:27

Mariia Mykhailova · Accepted Answer · 2020-07-22T09:20:41.083

5

Apply a CNOT gate with one of the qubits as control and the other as target. You'll get

$$\frac{1}{\sqrt{2}}(|0\rangle+e^{i\theta}|1\rangle) \otimes |0\rangle$$

Use the methodology from How to get the relative phase of a qubit? for the first qubit :-)

edited Jul 22 '20 at 09:20

answered Jul 22 '20 at 03:56

Mariia Mykhailova

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Hmm I tried that in the simulator but for some reason it didn't work. Then most likely its just a silly-mistake type issue with the way I wrote it. Thanks – Rehaan Ahmad Jul 22 '20 at 05:36
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Shouldn't it be the state after CNOT $\frac{1}{\sqrt{2}}(|0\rangle + e^{i\theta}|1\rangle)\otimes |0\rangle$? – Martin Vesely Jul 22 '20 at 06:49
@MartinVesely Fixed, thank you - a typical off-by-one error :-) – Mariia Mykhailova Jul 22 '20 at 09:21

How to get the relative phase of an entangled pair of qubits

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