I've just started to learn Quantum Computing and, to do it, I'm reading the course "Introduction from Quantum Computing" by IBM.

Now, I'm reading the chapter "Entangled states", section "Entangled states" where I have found the formula:

$$|\Phi\rangle=\frac{1}{\sqrt 2}\begin{bmatrix} 1 \\ 0 \\ 0 \\ 1 \end{bmatrix}=\frac{1}{\sqrt 2}(|00\rangle+|11\rangle).$$

They say about this state vector:

There are no pairs of single qubit states $|a\rangle$ and $|b\rangle$ whose product state would look like this.

But I don't understand it. Why there are no pairs of single qubits? It is because both qubits are on state 0 and 0 at the same time, isn't it?

I've just started to learn Quantum Computing and, to do it, I'm reading the course "Introduction from Quantum Computing" by IBM.

Now, I'm reading the chapter "Entangled states", section "Entangled states" where I have found the formula:

$$|\Phi\rangle=\frac{1}{\sqrt 2}\begin{bmatrix} 1 \\ 0 \\ 0 \\ 1 \end{bmatrix}=\frac{1}{\sqrt 2}(|00\rangle+|11\rangle).$$

They say about this state vector:

There are no pairs of single qubit states $|a\rangle$ and $|b\rangle$ whose product state would look like this.

But I don't understand it. Why there are no pairs of single qubits? It is because both qubits are on state 0 and 1 at the same time, isn't it?