Bloch sphere Definition and 21 Threads

QM uses separable Hilbert spaces as model to represent quantum system's states. Take for instance a 1/2-spin particle: its quantum pure state is represented by a ray in the abstract Hilbert space ##\mathcal H_2## of dimension 2. Take an observable represented by an Hermitian unitary operator...

I am reading a PHD thesis online "A controlled quantum system of individual neutral atom" by Stefan Kuhr. In it on pg46, he has a Hamiltonian I am also reading a book by L. Allen "optical resonance and two level atoms" in it on page 34 he starts with a Hamiltonian where the perturbation is...

Well, I have no clues for this problem. Since I can get nothing from the definition of ##\rho##, I tried from the right part. Also, I know that ##\left ( \vec r \cdot \vec \sigma \right ) ^2={r_1}^2 {\sigma _1}^2+{r_2}^2 {\sigma _2}^2+{r_3}^2 {\sigma _3}^2##. Plus, ##\rho## is positive; then...

I've read that ##\left | \psi \right > =cos \frac \theta 2 \left | 0 \right > + e^{i \phi} sin \frac \theta 2 \left | 1 \right >##, and the corresponding point in the Bloch sphere is as the fig below shows. I think ##\left | 0 \right >## and ##\left | 1 \right >## are orthonormal vectors...

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...

I am pretty sure that I would be comparing apples and oranges in this question, but as I usually learn something from the responses telling me in detail that my question is silly, here goes: Does the phase used as a weight in Feynman's path integral formulation (i.e., the quantum action S in...

If I construct a set of qubit gates, say {G1, G2 ... Gk ... Gn}, that can act on a state |ψ>, what does it mean for the set of states Gk |ψ> to span the Bloch sphere? As an example, take the set {G1, G2, G3, G4} = { I, X π/2 , Y π/2, Xπ } Here, X π/2 denotes a π/2 rotation about the x-axis, Y...

Hey, (I have already asked the question at http://physics.stackexchange.com/questions/244586/bloch-sphere-interpretation-of-rotations, I am not sure this forum's etiquette allows that!) I am trying to understand the following statement. "Suppose a single qubit has a state represented by the...

I found a funny model of the qubit written by Aerts in Foundations of quantum physics: a general realistic and operational realistic and operational approach. At the beginning the qubit is at the point P on the Bloch sphere. It will be measured along another direction (two opposite points on...

This question is mostly about group theory but I would like to understand it in the context of qubits rotating in a Bloch Sphere. What my understanding of things are right now: In the rotation Lie Group ##SO(3)##, we have three free parameters (##\frac{n(n-1)}{2}##), and this is also why we end...

Can anyone explain to me why the following operators are rotation operators: \begin{align*}R_x(\theta) &= e^{-i\theta X/2}=\cos(\frac{\theta}{2})I-i\sin(\frac{\theta}{2})X= \left(\!\begin{array}{cc}\cos(\frac{\theta}{2}) & -i\sin(\frac{\theta}{2}) \\ -i\sin(\frac{\theta}{2})&...

Homework Statement What is reduced density matrix ##\rho_A## and the Bloch vector representation for a state that is 50% ##|0 \rangle## and 50% ##\frac{1}{\sqrt{2}}(|0 \rangle + |1 \rangle)##Homework Equations The Attempt at a Solution [/B] I haven't seen many (any?) examples of this so I'm...

Homework Statement The problem is as follows. I have two spins, m_S and m_I. The first spin can either be \uparrow or \downarrow , and the second spin can be -1, 0 or 1. Now, I envision the situation as the first spin being on the bloch sphere, with up up to and down at the bottom. What I...

I'm having a bit of a brain fart here, so hopefully someone can help. Consider a closed, two-level quantum system. We know we can describe pure states as \alpha |0\rangle + \beta |1 \rangle for some orthonormal basis |0\rangle, |1 \rangle . The normalization conditions means we can...

I have a general question about extracting information from measurement of a qubit. Theoretically a qubit in a superposition state contains an infinite amount of information, but when measured collapses to a definite state and result. My question is this: Is there a way to obtain a value from...

Hey guys, I'm attempting to map some discrete points on the surface of the Bloch sphere: For instance, the full spectrum of ranges for variable theta is 0 < theta < pi. However, my goal is to limit that range from some theta_1 < theta < theta_2. I was going to use a spherical harmonic...

There is something that I don't quite understand in relation to the Bloch Sphere representation of qubits. I've read that any vector on the sphere is a superposition of two basic states, like spin up and spin down, denoted by |1> and |0>. So does this mean that if the vector is at z=0...

The Bloch sphere helps understanding the mathematical results for a one-spin state. One could think of the state as a spin pointing in direction \hat{n}. Then the probability for measureing the spin in the direction \hat{m} is simply P=|<\hat{m}|\hat{n}>|^2=\frac{1+\hat{n}\cdot\hat{m}}{2} and...

Hi could someone please explain the what the bloch sphere representation of a quantum state is useful for? thanks Mark

I am reading Quantum Computation and Quantum Information by Nelson and Chuang myself and came across the Bloch Sphere representation of a quibit on page 15 (equation 1.4) as: |\psi> = \cos\frac{\theta}{2} |0> + e^{i\psi}\sin\frac{\theta}{2} |1> I have two questions: 1. What is the motivation...

I have one critical problem with quantum computing. When I have one quantum state on bloch sphere, I do some transformation on that state for example PauliX transformation. As far as I know, we can present quantum state as |y> = cos (theta/2) |0> + e^(i*phi) sin (theta/2) |0> So if we...