# Does entanglement only exist between pairs of qubits?

I have read a bit in qiskit course so far.

Why entanglement state always represent with 2-qubit? Why not 3-qubit or 1-qubit only?

I do know that entanglement state happened when it can't represent with product state.

But I don't know the reason why entanglement state required atleast 2-qubit.

Is it because requires two operand when multiplying state vector?

• Advanced topic but related: Monogamy of entanglement You can have as many number of qubits entangled but there are caveats. Oct 15, 2022 at 9:30
• Oct 17, 2022 at 18:03

In simple words, the entanglement means that state of one quantum system is linked with state of another system. This naturally means that you need at least two systems (or qubits) to create the entanglement. Of course, you can have entanglement among as many qubits as you want, however, at least two. A nice example of more than two entangled qubits states are GHZ states $$\frac{1}{\sqrt{2}}(|0\dots 0\rangle + |1\dots 1\rangle).$$
Concerning product states. Such states can be described as tensor product of single-qubit states prepared with single qubit gates. This means that there is no link among the qubits and they are not entangled. An example of such state is uniformly distributed superposition where any basis state of $$n$$-qubit system has same probability amplitude. You can prepare this state by application of Hadamard gate (Hadamard is single qubit operation) on each of $$n$$ qubits, formely on state $$|0\rangle$$. As no two-qubit gate is involved, the entanglement does not occur.