[Quantum Computing] Quantum Parallelism State Calculation

[llha]

TL;DR Summary

Nielsen and Chuang state calculation isn't the full tensor product? But a full tensor product would be useless to measure?

Hi, I'm going through Nielsen and Chuang's Quantum Computation and Quantum Information textbook and I don't really understand this part about quantum parallelism:

Shouldn't the resulting state be (1/sqrt(2^4)) * (|0, f(0)> + |0, f(1)> + |1, f(1)> + |1, f(0)>), since the resulting state would be the (normalized) tensor product of (1/sqrt(2)) * (|0> + |1>) and (1/sqrt(2)) * (|f(0)> + f(1)>)?

I understand that would be pretty useless to measure, so I know I'm wrong, but I don't understand where I'm going wrong. Thanks in advance.

 

[Gaussian97]

A state of two qubits can be written in the base $\left|00\right>, \left|01\right>, \left|10\right>, \left|11\right>$. I would recommend you to apply the operator over these 4 states such that you really understand how the operator works, after that you can write the initial state as a linear combination of those states and use linearity and the previous result to get the final state.