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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How can I calculate this equation if we know that there is non zero Berry-phase between the valence and conduction band
The geometric phase can be interpreted as a Berry curvature in the momentum space. My guess is $(q^2+\text{Berry-phase}/\text{lattice constant}^2)/\text{direct gap}$.
$$\langle\psi_{n',\mathbf{k}+\...
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Hamiltonian representation of rotations for QuTiP Master Equation Solver
The unitary time evolution operator is given by
$$\hat{U}(t)=\exp[-\frac{it}{\hbar}\hat{H}]$$
Meanwhile, the rotation operator about some axis along the unit vector $\vec{n}$ for a spin-1/2 system ...
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Confusion regarding Bloch Sphere [closed]
$|Ψ> = 1/√2|0> + i/√2|1>$ (in $+i$ axis)
$α = 1/√2$ , $α^2 = 0.5$
$β = i/√2$ , $β^2 = -0.5$
$α^2 + β^2 = 1$
Ηere,
$α^2 + β^2 = 0$
How is this possible?
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Non-Monochromatic Bloch Equation
Is there literature on the Bloch equations with non-monochromatic radiation field? I.e. for a system with interaction Hamiltonian of the form $H_I = g \vec{E} \cdot \vec{\sigma} \sum_{i} a_i \cos(\...
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What identifies a surface on the Bloch sphere as corresponding to a subspace?
Given a Hilbert subspace, if you normalize every vector and then plot them all on the Bloch sphere (project them all onto the Bloch sphere), you'll get some surface. Do that for every (closed) ...
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Non-physical state in tomography
In tomography, we can use Pauli operators to estimate the qubit state, and by performing a substantial number of measurements one can estimate their expectation values. Define the estimates as $\bar\...
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Bloch Equations in a Rotated Frame
Consider the following Bloch equations in the absence of relaxation
$$
\frac{dM_x}{dt}=(\mathbf{M}(t)\times\mathbf{B}(t))_x, \ \ \ \ \ \ \frac{dM_y}{dt}=(\mathbf{M}(t)\times\mathbf{B}(t))_y,\ \ \ \ \ \...
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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 ...
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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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Directly get tangent vector of Bloch sphere from quantum state (qubit)?
We know that Bloch sphere is a good way to represent a qubit(two energy quantum systems). Now I want to know the tangent vector in Bloch sphere, e.g. for states $\frac{1}{\sqrt{2}}\left( \begin{array}{...
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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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States $-|0\rangle$ and $i|0\rangle$ in Bloch Sphere?
I am new on quantum computing and starting reading a book about it. Going through it, the Bloch sphere was described for two states.
My question about is: where are the states $-|0\rangle$ and $i|0\...
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Bloch sphere representation - rewriting a state
If a quantum state can be represented as
$$|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$$
Then
Because of $|\alpha|^2+|\beta|^2=1$, we may rewrite Equation (1.1) as $$|\psi\rangle=e^{i\gamma}\left(\...
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Is the Bloch sphere a bad way to visualize a qubit?
When a qubits is in a quantum state it can be measured as $[0\rangle$ or $[1\rangle$. Then why does the Bloch sphere have these two states on antipodal sides of the spheres? If I want to plot the ...
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What is the topology of non-entangled states region for a 2 qubit Bloch hypersphere?
Preamble
A two qubit/spin-1/2 system can be represented as
$$|\psi\rangle=\alpha|\uparrow\uparrow\rangle+\beta|\uparrow\downarrow\rangle+\gamma|\downarrow\uparrow\rangle+\delta|\downarrow\downarrow\...
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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 ...
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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 ...
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Optimal control for single qubit gate
Suppose we want to implement a single qubit gate $U$ and are only able to apply rotations around axes in the $xy$ plane of the Bloch Sphere, i.e. we can only apply Hamiltonians of the form
$$H(t) = \...
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Can 2-qubit systems be represented in the Bloch sphere representation?
I am studying a system with 2 qubits, so I need, for a given state, a Bloch representation for each qubit.
I am having difficulties because I get results that do not have sense at all. For example if ...
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Which paper introduced the concept of the "Bloch sphere"?
Everyone loves Bloch sphere, but which paper of Bloch was it introduced? The Wikipedia article on Bloch sphere (here), as of 17/May/2021 links to this paper of Bloch “Nuclear Induction” but it doesn’t ...
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Can pure qubit states be represented in a unit circle in $\mathbb R^2$? How does such representation relate with the Bloch sphere?
In this video they are regarding 2D circles denoting real-valued states of qubit, like
Teacher says it can be extended to 3D to Bloch sphere.
But Bloch sphere has |0> at the top and |1> at the ...
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Sketching dynamics of Bloch vector for ground state with dynamics induced by Hamiltonian
How can I sketch a Bloch vector for a system that is in the ground state |g> that is induced by Hamiltonian $ H_x = \frac{ω_x}{2}σ_z$? Is there a general method that I can follow for drawing Bloch ...
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Procedure to cut an Harmonic oscillator to two first level to obtain a qubit
Let us consider a (quantum) Harmonic oscillator:
$$H=\frac{p^2}{2m}+\frac{1}{2} m \omega^2 x^2$$
Using the annihilation/creation operators defined as:
$$a=\sqrt{\frac{\hbar}{2 m \omega}}(x+\frac{i}{m \...
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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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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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What is the physical intuition for Bloch Sphere? [duplicate]
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 ...
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