Plotting mixed state on Bloch sphere

[machi...@gmail.com]

Hi,

I'm trying to make a plot representing an (increasingly) mixed state on the Bloch sphere.
Both for the Bloch() and Bloch3d() class, I see some rescaling of the z-component of the vector, even though I only vary the y-component.

Here is an example:
z=0.75
y=0.911

vecs=[
[0,0*y,z],
[0,y*0.5,z],
[0,0.75*y,z]]
sphere = Bloch()
sphere.view=[90,0]
sphere.add_vectors(vecs)
sphere.show()

I also tried to input a few density matrices in the Bloch 3d class (using the add_states function) with constant z, decreasing x and got a similar result.
(see two pictures).

Any suggestions?

Best,

Machiel

[jrjoh...@gmail.com]

Hi Machiel

Thanks for your bug report. I agree that this seems strange, and it is probably a bug. I would guess that the following lines of code in the Bloch.plot_vectors

https://github.com/qutip/qutip/blob/master/qutip/bloch.py#L437-L439

instead should read something like

   xs3d = self.vectors[k][1] * array([0, 1])

   ys3d = -self.vectors[k][0] * array([0, 1])

   zs3d = self.vectors[k][2] * array([0, 1])

Rob

[Paul Nation]

This is because the length of the vector is calculated using sqrt(x**2+y**2+z**2).  Therefore your vector length is changing.  For a given state vector, the components of the Bloch vector are x=Tr(rho*sigmax),y=Tr(rho*sigmay),…

Therefore the total vector length is calculated like above.  But perhaps for the input of vectors, we could change this?

---------------------------------------
Paul D. Nation
Assistant Professor
Korea University
Department of Physics
Anam-dong 5, Seongbuk-gu
Seoul 136-713, South Korea
Email: pna...@korea.ac.kr
Phone: +82-02-3290-3092
Web:   nqdl.korea.ac.kr
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Attachments:

[Machiel Blok]

Hi Robert,
Yes thanks, that fixed it