i need help....please
If you Fourier sample the state 1/√22(|000>−|001>+|010>−|011>+|100>−|101>+|110>−|111>), which of the following states can be the outcome of your measurement? Select all that apply.
1. |000>
2. |001>
3. |010>
4. |011>
5. |100>
6. |101>
7. |110>
8. |111>
please answer this question
do you have any clue about this?
To determine which states can be the outcome of the measurement, we need to perform a Fourier transform on the given state.
The Fourier transformation of a single-qubit state is given by:
|0⟩ -> 1/√2(|0⟩+|1⟩)
|1⟩ -> 1/√2(|0⟩-|1⟩)
Applying these transformations to each qubit in the given state:
1/√22(|000>−|001>+|010>−|011>+|100>−|101>+|110>−|111>)
1/√22[1/√2(|000⟩+|001⟩) - 1/√2(|010⟩+|011⟩) + 1/√2(|100⟩+|101⟩) - 1/√2(|110⟩+|111⟩)]
Expanding the above expression, we get:
1/√8 ( |000⟩ + |001⟩ - |010⟩ - |011⟩ + |100⟩ + |101⟩ - |110⟩ - |111⟩ )
Now we can see that the coefficients of each state are 1/√8, and the states are the exact same as the given options. So, the possible outcomes of the measurement are:
1. |000⟩
2. |001⟩
3. |010⟩
4. |011⟩
5. |100⟩
6. |101⟩
7. |110⟩
8. |111⟩
Therefore, all the given states can be the outcome of the measurement.