# A question about notation for quantum states

I am reading an article on representation of digital images using qubits. But I am not able to understand the notations of the article. Can somebody help me: $$|0\rangle$$: It means the first basis vector in the respective vector space. But what does $$|0\rangle^{3q+ 2n}$$ mean?

A single qubit in the $$0$$ state is often written as $$|0\rangle$$.
If we have two independent qubits in the zero state we can write them as $$|0\rangle\otimes|0\rangle$$. This is often also written as $$|0\rangle|0\rangle = |00\rangle =|0\rangle^{\otimes2}=|0\rangle^2$$. This extends naturally to more qubits.
Coming back to your question: $$|0\rangle^{\otimes 3q+2}$$ (or $$|0\rangle^{3q+2}$$), it are just $$3q+2$$ qubits, all in the zero state $$|0\rangle$$.
Also, think about the dimensions these basis vectors are creating. $$|0\rangle$$ is a $$2\times 1$$ vector, which is in the standard basis looks like: $$\begin{bmatrix} 1\\0 \end{bmatrix}$$Then, continuing $$|0\rangle^{\otimes2} = |00\rangle=|0\rangle|0\rangle = |0\rangle \otimes |0\rangle = \begin{bmatrix} 1\\0 \end{bmatrix} \otimes \begin{bmatrix} 1\\0 \end{bmatrix} = \begin{bmatrix} 1\\0\\0\\0 \end{bmatrix}$$