# Questions tagged [bloch-sphere]

A geometrical representation of the pure state space of a two-level quantum mechanical system (qubit), used in quantum mechanics and computing.

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### How can the Bloch sphere, built from one complex dimension, specify 2-complex dimensional Pauli spinors?

Two-component spinors can be identified with points on the surface of the Bloch Sphere. The Bloch sphere is constructed from the 1-complex-dimensional complex plane plus the point at infinity. How ...
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### How is the inner product of two quantum states related to their associated Bloch vectors?

I have a doubt about how two equivalent ways of calculating the inner product between two states seem to not be actually equivalent, as they should. In particular, I'm interested in the case where the ...
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### Are qubits just analog, continuous classical bits?

Topologically, classical bits (cbits) are essentially special cases of qubits restricted to the poles of the Bloch sphere. However, this restriction doesn't seem to be classical per se, but is simply ...
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### Finding $\theta$ and $\phi$ when qubit state is $\frac{1}{\sqrt 2}[i ,1]^T$

Because we know the state of a qubit can be described as: $$|q\rangle=\cos{\frac{\theta}{2}}|0\rangle+e^{i\phi}\sin{\frac{\theta}{2}}|1\rangle\\\ \\ \theta, \phi \in \mathbb{R}$$ How do I find the ...
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### How do I visualize a stepwise rotation on the Bloch Sphere using $SO(3)$ and $SU(2)$?

Searching for an implementation (that helps me to understand how $SO(3)$ and $SU(2)$ relate to each other) I came across this interesting question Visual interpretation, on the Bloch sphere, when ...
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### Find coefficient for pure and mixed states

Consider a generic $2\times 2$ Hermitian matrix written as $$\rho =\alpha\sigma_0+\beta\hat{\vec n}\cdot\vec\sigma\quad ,$$ where $\hat{\vec n}$ is a unit vector and the coefficients are real numbers. ...
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### How to prove that every mixed one-qubit state admits a Bloch-sphere representation? [duplicate]

A mixed state $\rho$ can be written as $$\rho=\frac{1}{2}\left(I+r_x\sigma_x+r_y\sigma_y+r_z\sigma_z\right)\qquad\left(\vec{r}:=\left(r_x,r_y,r_z\right)^T\in\mathbb{R}^3; ||\vec{r}||\leq 1\right)$$ ...
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### Quantum Computer - Rotation Bloch Sphere [closed]

please can anyone help? What gate combination allows moving from the state between |0> and |1> states. In terms of bloch-sphere from the north pole to the south pole as an example. And how can ...
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### Understanding the Bloch Sphere Better

Numerous times I have used the Bloch sphere and visualized gates as rotations. For Z and X rotations, it is a pretty good representation. However, today I found that this does not stand for Y/2 gate. ...
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