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3 votes

Solving a Bloch sphere where alpha is imaginary

The bloch sphere can be confusing and intimidating for sure. There are a couple of key things I always try to remember when I want to work with it. Euler's formula is always our friend: $e^{ix}=\cos{...
6 votes
Accepted

How is the surface of a Bloch sphere a Hilbert space?

The surface of a Bloch sphere is not a Hilbert space. Maybe they meant to write that it's a valid projective Hilbert space (in particular it's isomorphic to $\mathbb{CP}^1$)? It's not a vector space, ...
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4 votes

Why are orthogonal quantum states represented as collinear in the Bloch sphere?

The Bloch representation of states is what you get when you decompose density matrices in terms of a basis of orthonormal Hermitian operators. That is, you write $\rho=\sum_k \sigma_k \langle\sigma_k,\...
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0 votes

Why are orthogonal quantum states represented as collinear in the Bloch sphere?

It is by the very definition of the Bloch sphere. Here is an illustration. You may go to try it at https://BigQubits.com/?x=0 yourself.
0 votes

Writing a Density matrix in terms of the magnitude of the Bloch Vector

It must be a typo. Remember that a density matrix must have trace 1, which yours does, and your expected answer doesn't.
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