# 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 you determine direction of spin-1/2 states?

How do you determine the direction of the state of a spin-1/2 particle? For instance, given the quantum state $|\psi\rangle=(1,0)$, where does this vector point in space? I would say that it points in ...
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### Comparison between Jones vectors and spin state vectors

I'm trying to learn about spinors by myself: I've found what it seems to me a very good series of videos on youtube which explains them starting from basic concepts and examples. Now, in this video, ...
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### Bloch's Theorem and its solutions

I was reading Ali Omar text on solid state course and it said about the fact that electrons in a lattice or in a periodic lattice never scatters or make collisions with the positive ion cores, as the ...
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1 vote
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### Physical Interpretation of the trace distance between Bloch vectors

I came across a problem in which the trace distance is maximum if the Bloch vectors of the two density matrices are perpendicular to each other. What is the physical interpretation of this?
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### Difference between Poincaré and Bloch sphere for single photons

The Bloch sphere is a geometrical representation of a two-levels quantum system, for example we can use it to represent the spin of a single qubit in the basis $\{\lvert H \rangle, \lvert V \rangle\}$....
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### How to apply the Bloch-Floquet theorem for a square lattice in a magnetic field?

Generalizing the question here, if I have a square lattice in the homogeneous magnetic field $B$ as the given picture, how can we apply the Bloch-Floquet theorem in this periodic structures (with the ...
1 vote
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### Do Bloch sphere rotations span $SU(2)$ (up to a global phase)? [duplicate]

It is well known that the Pauli group $\{I,X,Y,Z\}$ spans the group of $2\times2$ unitary matrices, $SU(2)$, for example see this link. A general Bloch sphere rotation by an angle $\alpha$ about an ...
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### How to write an arbitrary qubit density operator? [duplicate]

Physics noob here: I am reading the Wikipedia on Density Matrices (https://en.wikipedia.org/wiki/Density_matrix), and in the section labeled "Pure and mixed states", it states "An ...
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1 vote
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### Is there a nice formula to represent POVMs $\Pi$ in a Bloch-vector-like form?

A way to write a quantum state is to use the Bloch vector representation, i.e., $$\varrho = \frac{1}{2}\left(\mathbb{I}_2 + \boldsymbol{r} \cdot \boldsymbol{\sigma}\right)$$ In general a POVM for a ...
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### Rabi Oscillations: $\pi$-Pulse vs a single photon

I am puzzled by the following: Assume an atom as a two-level-system. A $\pi$-Pulse acting on an atom in the ground state promotes this atom in the excited state. This is done by a continuous ...
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### What is the physical significance of phase difference in qubit or spin half? [duplicate]

Whenever it is talked about phase difference or lack of it, double slit example is used as the example. But I want to know what is the physical manifestation of phase difference for a qubit (or spin ...
1 vote
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### 90 degree rotation about $z$-axis on Bloch sphere

I am a beginner on quantum information and right now I study it from the lectures by Peter Shor. The lectures can be found on edX and can be viewed on YouTube as well. The lecture that I'm struggling ...
1 vote
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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 (... 85 views

### 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 ...
1 vote
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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 ... 155 views

### 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 ...
I am very confused about how to think about the Bloch Sphere. How can we relate the concept of expectation value to the Bloch sphere? If my state lies in let's say $yz$ plane how can we say that ...