I [Quantum Computing] Quantum Parallelism State Calculation

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The discussion centers on the confusion regarding quantum parallelism and the calculation of the resulting state in a quantum system. The user questions the normalization of the state, suggesting it should be a tensor product of two states, but recognizes a misunderstanding in the measurement implications. A recommendation is made to apply the operator over the four basis states to clarify the operator's function. This approach aims to help the user derive the final state correctly by utilizing linearity. Understanding these concepts is crucial for grasping quantum parallelism in quantum computing.
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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:
1626469417681.png


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.
 
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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.
 

Thread 'Angular Momentum Vector and Its Magnitude'

For the quantum state ##|l,m\rangle= |2,0\rangle## the z-component of angular momentum is zero and ##|L^2|=6 \hbar^2##. According to uncertainty it is impossible to determine the values of ##L_x, L_y, L_z## simultaneously. However, we know that ##L_x## and ## L_y##, like ##L_z##, get the values ##(-2,-1,0,1,2) \hbar##. In other words, for the state ##|2,0\rangle## we have ##\vec{L}=(L_x, L_y,0)## with ##L_x## and ## L_y## one of the values ##(-2,-1,0,1,2) \hbar##. But none of these...
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