How Do You Transform Qubit States Between Different Bases on the Bloch Sphere?

[xwkkx]

Anyone know how to change a basis of a qubit state of bloch sphere given a general qubit state? There are 3 different basis corresponding to each direction x,y,z where |1> ,|0> is the z basis, |+>, |-> is the x basis and another 2 ket notation for y basis.

Given a single state in the x basis |0> and |1>, how do i change it to the z basis? I know I need to apply a matrix operator to it but what is it? And also for changing to y basis. Thanks for help

 

[PeterDonis]

There are 3 different basis

Actually there are an infinite number of possible bases. Heuristically, you can think of the "direction" of the basis pointing anywhere you like on the sphere; there are an infinite number of directions it can point. The x, y, and z directions are just three of them that happen to be often used for examples.

Given a single state in the x basis |0> and |1>, how do i change it to the z basis?

First, you used |0> and |1> to denote the basis states of the z basis in the first paragraph of your post, contradicting what you wrote in the second paragraph, quoted just above. So you need to make up your mind about your notation.

That said, if we use the notation in your first paragraph, so |0> and |1> are the z basis states, do you know how to write the x basis states, |+> and |->, in terms of them? How about the y basis states?