the statement “The quantum state of a qubit is obtained by reading across a row … |0011>” seems quite problematic to me.
First, the quantum (pure) state of the considered qubit is a priori not well defined any more at this stage, the global state of the 7-qubits register must be considered as a whole because of entanglement (see next chapter)
Second, even if we could assign this qubit a well defined quantum state, using the notation “0011>” for it is very misleading, as this is used also for the tensor product of qubit states…