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I am experimenting with concepts in Quantum Computing and I have landed on using entangled Qubits to perform certain actions.

My question is this: is it possible to have (let's say) 3 entangled Qubits in a system. If it is, then how much information is retrievable/usable when only 2 of these Qubits are measured? The application I am thinking of is using 2 of the 3 Qubits for a one-time access code and then the 3rd becomes useless (and almost automatically gets locked out).

I realise my mathematics is basic but it is the application I am curious about.

Any help would be appreciated.

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    $\begingroup$ Hi Stephen! Welcome to QCSE! When we have three entangled qubits, we usually like to think of them either in the GHZ state $\frac{1}{\sqrt{2}}(\vert 000\rangle+\vert 111\rangle)$ or in the W state $\frac{1}{\sqrt{3}}(\vert 001\rangle+\vert 010\rangle+\vert100\rangle)$.... (more) $\endgroup$
    – Mark Spinelli
    Nov 14, 2019 at 14:52
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    $\begingroup$ If your qubits are in the GHZ state in the standard basis, then measuring only two of them will tell you fully about the other one. Similarly, if you qubits are in the W state in the standard basis, then upon measuring your two qubits, this is enough information for you to determine the other one. The Wikipedia articles on the W and GHZ states are pretty good - can you consider reviewing them, and editing/revising your question in light of the Wikipedia articles, if you have questions about them to which you are uncertain? $\endgroup$
    – Mark Spinelli
    Nov 14, 2019 at 15:02
  • $\begingroup$ see also multipartite entanglement $\endgroup$
    – glS ♦
    Nov 14, 2019 at 18:09

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Here is a circuit for preparation of state $\frac{1}{\sqrt{2}}(|000\rangle + |111\rangle)$.

GHZ state

And here one for state $\frac{1}{\sqrt{3}}(|001\rangle + |010\rangle+ |100\rangle)$

W state

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There is entanglement of formation and entanglement that can be distilled, but the question of how to measure the entanglement of more than 2 qubits is an ongoing area of research. Yes, you can have three-qubit entanglement. For example, the GHZ state (like the Bell states, complete correlation among the qubits) or the W state. In the GHZ state, if you measure one qubit in the z direction, you lose all entanglement. In the W state, if you measure one qubit, the other two remain entangled.

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  • $\begingroup$ I suppose you mean measure in the computational basis? In you measure the GHZ state in the X basis then you'll have a maximally entangled state on the other qubits conditioned on the outcome. $\endgroup$
    – Rammus
    Oct 17, 2022 at 18:24
  • $\begingroup$ @Rammus, thanks, I agree! I amended the answer. $\endgroup$
    – Bennett Brown
    Oct 22, 2022 at 0:55

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