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Post Closed as "Duplicate" by Mark Spinelli, Adam Zalcman, CommunityBot
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glS ♦
glS ♦
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Finding the polar and azimuthal angles of a blochthe Bloch vector corresponding to $\frac1{\sqrt2}(1-i)|0\rangle-\frac i{\sqrt2}|1\rangle$

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Spacetoon
Spacetoon
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I need to find the polar angles and azimuthal angles of the following bloch vector:

$$ \frac{1-i}{2}|0\rangle - \frac{i}{\sqrt{2}}|1\rangle $$

I just couldn't figure it out, and I could also not find out how I could factor out the global phase, can anyone here please help?

I got to the point where I knew that $\cos(\frac{\theta}{2}) = \frac{1-i}{2}$ and $\sin (\frac{\theta}{2}) e^{e^{i\phi}} = -\frac{i}{\sqrt{2}}$$\sin (\frac{\theta}{2}) e^{i\phi} = -\frac{i}{\sqrt{2}}$, I'm guessing I have to factor out some global phase here and ignore it in order to solve the equations, but I couldn't figure it out. I've tried looking elsewhere for methods on how to solve this, but could not find it.

I need to find the polar angles and azimuthal angles of the following bloch vector:

$$ \frac{1-i}{2}|0\rangle - \frac{i}{\sqrt{2}}|1\rangle $$

I just couldn't figure it out, and I could also not find out how I could factor out the global phase, can anyone here please help?

I got to the point where I knew that $\cos(\frac{\theta}{2}) = \frac{1-i}{2}$ and $\sin (\frac{\theta}{2}) e^{e^{i\phi}} = -\frac{i}{\sqrt{2}}$, I'm guessing I have to factor out some global phase here and ignore it in order to solve the equations, but I couldn't figure it out. I've tried looking elsewhere for methods on how to solve this, but could not find it.

I need to find the polar angles and azimuthal angles of the following bloch vector:

$$ \frac{1-i}{2}|0\rangle - \frac{i}{\sqrt{2}}|1\rangle $$

I just couldn't figure it out, and I could also not find out how I could factor out the global phase, can anyone here please help?

I got to the point where I knew that $\cos(\frac{\theta}{2}) = \frac{1-i}{2}$ and $\sin (\frac{\theta}{2}) e^{i\phi} = -\frac{i}{\sqrt{2}}$, I'm guessing I have to factor out some global phase here and ignore it in order to solve the equations, but I couldn't figure it out. I've tried looking elsewhere for methods on how to solve this, but could not find it.

I added my steps so far.
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Spacetoon
Spacetoon
  • 23
  • 4

I need to find the polar angles and azimuthal angles of the following bloch vector:

$$ \frac{1-i}{2}|0\rangle - \frac{i}{\sqrt{2}}|1\rangle $$

I just couldn't figure it out, and I could also not find out how I could factor out the global phase, can anyone here please help?

I got to the point where I knew that $\cos(\frac{\theta}{2}) = \frac{1-i}{2}$ and $\sin (\frac{\theta}{2}) e^{e^{i\phi}} = -\frac{i}{\sqrt{2}}$, I'm guessing I have to factor out some global phase here and ignore it in order to solve the equations, but I couldn't figure it out. I've tried looking elsewhere for methods on how to solve this, but could not find it.

I need to find the polar angles and azimuthal angles of the following bloch vector:

$$ \frac{1-i}{2}|0\rangle - \frac{i}{\sqrt{2}}|1\rangle $$

I just couldn't figure it out, and I could also not find out how I could factor out the global phase, can anyone here please help?

I need to find the polar angles and azimuthal angles of the following bloch vector:

$$ \frac{1-i}{2}|0\rangle - \frac{i}{\sqrt{2}}|1\rangle $$

I just couldn't figure it out, and I could also not find out how I could factor out the global phase, can anyone here please help?

I got to the point where I knew that $\cos(\frac{\theta}{2}) = \frac{1-i}{2}$ and $\sin (\frac{\theta}{2}) e^{e^{i\phi}} = -\frac{i}{\sqrt{2}}$, I'm guessing I have to factor out some global phase here and ignore it in order to solve the equations, but I couldn't figure it out. I've tried looking elsewhere for methods on how to solve this, but could not find it.

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Spacetoon
Spacetoon
  • 23
  • 4