Vectors along Bloch sphere

Vectors along Bloch sphere

par Yago Pérez Pérez,
Nombre de réponses : 3


I'm having visualizing these vectors along the Bloch sphere, I get that the "up" is essentially +1 in vertical axis, and "down" is -1, but I don't understand how the i interferes with all that. Because for the first case, if there was no i , I believe that would simply correspond the 0 vector no?


En réponse à Yago Pérez Pérez

Re: Vectors along Bloch sphere

par Victor Braun,
Each ket is a point on a sphere. The zero vector doesn't lie on the sphere and thus cannot represent a ket. Here, don't forget the 1/sqrt2, which is the cos and sin of pi/4, so here the ket is the point with angles theta=pi/2 (2*pi/4) and phi=pi/2. With no i, you simply have a different x,y phase and phi=0.
So in the first case, it is the + eigenket of Y and with no i, the + eigenket of X.

Hope it helps! :)

IMPORTANT NOTE: the Bloch sphere is a visualization, don't mix ket superposition and bloch sphere vectors operations as the mapping is not linear (adding two kets != adding two vectors in the BS)
En réponse à Yago Pérez Pérez

Re: Vectors along Bloch sphere

par Elyes Ben Chaabane,
You should check out the document "LECTURE NOTES" chapiter 2.10 "la sphère de bloch" figure 2.14 page 44 and 45, that figure will help you visualize the vector inside of the sphere or you can convert it into a state of the form cos(theta) |0> + sin(theta) exp(i phi) |1> where theta and phi are angles, thus you will now the direction of your vector with coordinates theta and phi (remember i = exp(i pi/2))