Linked Questions

2 votes
3 answers
190 views

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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3 votes
1 answer
266 views

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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14 votes
3 answers
2k views

Up and down spin are orthogonal, not antiparallel

In conventional coordinate systems (anything you solve a simple Newtonian mechanics problem with), up and down are + and - z. A vector pointing up and a vector pointing down are anti-parallel. But in ...
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4 votes
2 answers
3k views

How are quantum qubits implemented? [duplicate]

Its very easy to pull a logic gate or transistor circuit of the internet for example and begin to understand how it represents physical bits, by either having 5V across the circuit or below 3.3V. But ...
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6 votes
5 answers
749 views

Interpretation of rotating a quantum state

I'm currently taking an introductory quantum mechanics course, where the last covered topic was spin and identical particles. During some reading online, I stumbled across the term "rotating a quantum ...
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1 vote
3 answers
2k views

How are linear combinations of qubit states represented in the Bloch sphere?

According to the Wikipedia article on the Bloch sphere, a pure state of a qubit can always be represented as $$| \psi \rangle = \cos \left( \frac{\theta}{2} \right)| 0 \rangle + e^{i \phi} \sin\left(\...
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0 votes
2 answers
1k views

Pauli matrices as measurement operators versus spin probability

Pauli matrices tell us what the spin of a particle is along a certain axis. Let's say I want to measure the spin along the z-axis then the pauli operator $$\sigma_z = \begin{bmatrix}1&&0\\0&...
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0 votes
1 answer
906 views

Bloch sphere representation of an eigenvector

I'm trying to work through a problem that wants me to determine the Bloch sphere representation of the eigenvectors of $\sigma_{z}$. I'm working in bra-ket notation so these would be $\ v_{+} = |0\...
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2 votes
3 answers
184 views

Quantum Mechanics Notation

I'm studying the Bloch Sphere and just wanted to ask what this notation means: $|\psi\rangle = \alpha|1\rangle$ for example I'm just not familiar with the notation in this context if anyone could ...
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5 votes
1 answer
768 views

How to understand Bloch sphere representation?

I'm really new to quantum computation. Now, I'm going through a tutorial article Quantum Computation: a Tutorial (NB: PDF). I was confused by certain points over there. So, on page 5, when the ...
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1 vote
3 answers
245 views

Determine the energy eigenstates and eigenvectors [closed]

Question: Let $\{\vert\psi_1\rangle, \vert\psi_2\rangle \}$ be an orthonormal basis. Define Hamiltonian $\hat{H} = \alpha \left( \vert\psi_1\rangle \langle\psi_2\vert + \vert\psi_2\rangle\langle\psi_1\...
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1 vote
1 answer
415 views

Bloch Sphere vs 2D hilbert Space

For a 2 level quantum system we can represent it in two ways: in 2D Hilbert space and also in the form of a Bloch sphere Now, In what space does the Bloch sphere lie? Are they equivalent? because ...
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1 vote
1 answer
110 views

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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1 vote
2 answers
382 views

Understanding quantum spin

I'm trying to get an idea of what spin in quantum mechanics means. I have the following questions regarding spin: The eigenvalues of the operator corresponding to the z component of spin is $\hat{S}_{...
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  • 883
0 votes
2 answers
161 views

Why are the eigenvalues of $S_x$, $S_y$, $S_z$ operators in Stern-Gerlach experiment for spin the same?

I get that $S_z$ operator has spin $\frac{h}{2\pi}$ ,$\frac{-h}{2\pi}$ because the spin angular momentum along the $z$ direction is the latter. But why should this be the same even for $S_x$. Can you ...
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  • 11

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