# What is the notation for factoring a state when non-adjacent qubits are entangled?

Suppose I have the entangled state

$$|\psi\rangle = \frac{1}{\sqrt{2}}(|000\rangle + |110\rangle).$$

If i want to factor the non-entangled parts of this state out, I can easily write that down as

$$|\psi\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle) \otimes |0\rangle.$$

Suppose now, however, that I have a state

$$|\phi\rangle = \frac{1}{\sqrt{2}}(|000\rangle + |101\rangle).$$

In $$|\phi\rangle$$, qubits $$1$$ and $$3$$ are entangled as opposed to qubits $$1$$ and $$2$$ in $$|\psi\rangle$$. Is there a notation for factoring out qubit $$2$$ in this state that is elegant like for $$|\psi\rangle$$?

$$\vert\phi\rangle=\frac{1}{\sqrt 2}(\vert 0_A0_B0_C\rangle +\vert 1_A0_B1_C\rangle)= \frac{1}{\sqrt 2}(\vert 0_A0_C\rangle +\vert 1_A1_C\rangle)\otimes \vert 0_B\rangle,$$
$$\vert\phi\rangle=\frac{1}{\sqrt 2}(\vert 000\rangle +\vert 101\rangle)= \frac{1}{\sqrt 2}(\vert 0.0\rangle +\vert 1.1\rangle)\otimes \vert .0.\rangle,$$