Why is My Calculation of Φ Incorrect?

[gremio594]

Homework Statement

The state

|ϕ⟩=(1−2√i)/4|0⟩−(3−2i)/4|1⟩
is measured in the Hadamard basis |+⟩, |−⟩. What is the probability to obtain |+⟩ as measurement result?

Relevant Equations

Pψ(v) = |<v|ψ>|^2

I calculated <+|Φ> to be (1-√2i)/4√2 + (3-2i)/4√2. When I squared this I for 16/32 but this is no the right answer.

 

[Gaussian97]

First of all, this state is not normalized, so you cannot compute the probability as $\left|\left<+\right|\left.\phi\right>\right|^2$.
I think probably you have a typo and the term $2\sqrt{i}$ should be $i\sqrt{2}$, then the state is normalized. But two questions:
1. How did you compute $\left<+\right|\left.\phi\right>$?
2. How did you square this complex number?

 

[gremio594]

First of all, this state is not normalized, so you cannot compute the probability as $\left|\left<+\right|\left.\phi\right>\right|^2$.
I think probably you have a typo and the term $2\sqrt{i}$ should be $i\sqrt{2}$, then the state is normalized. But two questions:
1. How did you compute $\left<+\right|\left.\phi\right>$?
2. How did you square this complex number?

 

[gremio594]

I was not adding the complex numbers together before trying to square them. After doing that I was able to get the right answer

 

[Gaussian97]

What answer did you get finally?

 

[gremio594]

What answer did you get finally?

I think it was (5-2√2)/16

 

[Gaussian97]

Ok, perfect