# 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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### Is the Poincaré sphere like the Bloch sphere (points inside)

Is there a close analogy in spectrometry between electrons inside the Bloch sphere and photons inside the Poincaré sphere? It seems that they are both in a mixed state. One can use photons or ...
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### Is the Bloch sphere a bad way to visualize a qubit?

When a qubits is in a quantum state it can be measured as $[0\rangle$ or $[1\rangle$. Then why does the Bloch sphere have these two states on antipodal sides of the spheres? If I want to plot the ...
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### Can 2-qubit systems be represented in the Bloch sphere representation?

I am studying a system with 2 qubits, so I need, for a given state, a Bloch representation for each qubit. I am having difficulties because I get results that do not have sense at all. For example if ...
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### Which paper introduced the concept of the "Bloch sphere"?

Everyone loves Bloch sphere, but which paper of Bloch was it introduced? The Wikipedia article on Bloch sphere (here), as of 17/May/2021 links to this paper of Bloch “Nuclear Induction” but it doesn’t ...
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### Can pure qubit states be represented in a unit circle in $\mathbb R^2$? How does such representation relate with the Bloch sphere?

In this video they are regarding 2D circles denoting real-valued states of qubit, like Teacher says it can be extended to 3D to Bloch sphere. But Bloch sphere has |0> at the top and |1> at the ...
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### Sketching dynamics of Bloch vector for ground state with dynamics induced by Hamiltonian

How can I sketch a Bloch vector for a system that is in the ground state |g> that is induced by Hamiltonian $H_x = \frac{ω_x}{2}σ_z$? Is there a general method that I can follow for drawing Bloch ...
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### A potential well with 3-fold reflection symmetry

When we are talking about Bloch's theorem and also the tight-binding approximation, we can use them to help finding eigenstates of a system. However, I am so confused how to apply it in this case (...
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### Time dependent perturbation theory on Bloch sphere

I have a Hamiltonian of the form: $\begin{pmatrix} E_1 & W_1(t)+iW_2 \\ W_1(t)-iW_2 & E_2 \end{pmatrix}$ Where $E_1,E_2,W_1,W_2$ are real and only $W_1$ is time dependent (it is actually ...
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### Trying to visualize the concept of qubits [closed]

Background Complete newbie, never taken a physics course. Question I'm trying to visualize the concept of qubits. Qubits can achieve a mixed state, called a "superposition" where they are ...
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### Pole point on the Bloch sphere

If the state of the qubit is a point at a pole on the Bloch sphere, does this mean that the coefficient of the component corresponding to the other pole is zero?
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### Vector from $SU(2)$ to $SO(3)$? [closed]

I know how to change the element(a matrix) in $SU(2)$ to the matrix in $SO(3)$, and I found one way to change the state(vector) from $2\times 1$ to $3\times 1$, but I don't know why. The method is ...
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### Hamiltonian with identity operator: how to visualize the (time-evolution) rotation?

For the Hadarmard Hamiltonian, $\hat H = (\hat X+\hat Z)/\sqrt 2$, where $\hat X$ and $\hat Z$ are Pauli matrices. The time evolution of a state under this Hamiltonian could be visualized by a ...
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### Bloch sphere representations for multi-qubit quantum systems

Just a short mixed quantum state representation question. Given a single qubit density matrix $\rho$, since the Pauli matrices form a basis for 2x2 complex matrices, the Bloch sphere representation ...
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### Average over the Bloch sphere

Consider you have a function of a two-level wave quantum state $f(\vert \psi \rangle )$, with $\vert \psi \rangle = \alpha \vert 0 \rangle + \beta e^{\rm i \phi} \vert 1 \rangle$. With no loss of ...
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### Why can we only perform rotations of the Bloch sphere (with unitary matrices), and not reflections?

It's easy to take a quantum state represented on the Bloch sphere and rotate it around an arbitrary ray emanating from the origin. On the other hand, we can never use a unitary matrix to get a ...
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### Outcomes of quantum measurements

I'm pretty new to quantum computing, and I'm wondering how I can compute the outcome of a projective measurement of a spin along the +Z axis followed by a projective measurement along the -Z axis. I ...
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### Why an element of $SU(2)$ acts as a rotation for the Majorana representation of states?

I recently asked a question in quantum computing stack exchange and as suggested by someone in the comments, I decided to ask my question here as well: I know that for a given spin-j quantum state, ...
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### Prove that qubits can be represented on a unit sphere, avoiding the density matrix formalism [duplicate]

The Bloch Sphere is regarded as the most "intuitive" way of explaining a 2-level quantum system in computation and rotations of states described on Bloch sphere provides a really easy ...
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### Quantum Computing without Complex Numbers

p.s. I am trying to get a handle on what actual computing operations a quantum computer program does. Any information on that would be appreciated [noting the issue that that might count as a ...
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### Consider the following single-qubit state on the Block sphere [closed]

$$\left| \varphi \right>=\frac{1+i}{\sqrt{3}} \left| 0 \right> + {\sqrt{\frac{1}{3}}} \left| 1\right>$$ I need to find the coordinate 𝜃, and ϕ values of the quantum state.
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### Does an stereographical projection of a physical plane have any physical meaning?

Mathematically, an arbitrary 2D plane can be mapped onto a sphere by stereographical projection. Each line on the plane is equivalent to each line on the sphere. If the sphere rotates under the $SO(3)$...
I am working now with spin-1 where I have instead of states $|{+1}\rangle$ and $|{-1}\rangle$, as for in spin-1/2 case, I have $|{+1}\rangle$, $|0\rangle$ and $|{-1}\rangle$. How can I check the ...