Linked Questions

2
votes
3answers
147 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 ...
3
votes
1answer
166 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 ...
4
votes
2answers
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 ...
5
votes
5answers
499 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 ...
1
vote
3answers
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(\...
0
votes
2answers
784 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&...
0
votes
1answer
709 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\...
2
votes
3answers
157 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 ...
5
votes
1answer
673 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 ...
1
vote
1answer
327 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 ...
1
vote
3answers
128 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\...
1
vote
2answers
316 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}_{...
1
vote
1answer
212 views

Are there natural geometrical representations for a qubit other than the Bloch sphere? [closed]

The Bloch Sphere is a geometrical representation of the state space of a qubit system. I'm wondering if there are other natural geometrical representations one could use as alternatives to the Bloch ...
1
vote
1answer
160 views

Determine the state $|\psi \rangle$

The question is: The angular momentum components of an atom prepared in the state $|\psi\rangle$ are measured and the following experimental probabilities are obtained: \begin{equation} P(+\hat{z}) = ...
2
votes
2answers
104 views

Why can't we infer the amplitude of the spin vector components from the spin probability when the latter is 50%?

I'm currently reading Quantum Mechanics: The Theoretical Minimum. I'm stuck trying to understand a minor point in the book where the authors seem to suggest that we can know the probability of ...

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