A geometrical representation of the pure state space of a two-level quantum mechanical system (qubit), used in quantum mechanics and computing.
Questions tagged [bloch-sphere]
114 questions
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Understanding the Bloch sphere
It is usually said that the points on the surface of the Bloch sphere represent the pure states of a single 2-level quantum system. A pure state being of the form:
$$
|\psi\rangle = a |0\rangle+b |1\rangle
$$
And typically the north and south poles…
user098876
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Why is $\theta \over 2$ used for a Bloch sphere instead of $\theta$?
I'm a beginner in studying quantum info, and I'm a little confused about the representation of a qubit with a Bloch Sphere. Wikipedia says that we can use $$\lvert\Psi\rangle=\cos\frac{\theta}{2} \lvert 0\rangle + e^{i\phi}\sin\frac{\theta}{2}…
Mike Wong
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Visual interpretation, on the Bloch sphere, when Hadamard gate is applied twice
It's known that the Hadamard operation is just a rotation of the sphere about the $\hat{y}$ axis by 90 degrees, followed by a rotation about the $\hat{x}$ axis by 180 degrees.
On the other hand, $H^{2}=I$, where $H$ is the unitary matrix…
study
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9
votes
1 answer
Characterisation of the generalised Bloch space in spherical coordinates
I'm so confused by the following definition in the "Quantum Error Correction" by Lidar and Brun that not even sure how to formulate the question properly.
Let $\mathbf n$ denote a unit vector, i.e., $\mathbf n\in \mathbb R^{d^2-1}$ and…
mavzolej
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votes
1 answer
Can we make a Bloch sphere for Weyl spinors?
If spinors are the "square root" of 3-vectors [$\mathrm{SU}(2)$ double cover of $\mathrm{SO}(3)$], Weyl spinors can be thought of as the "square root" of 4-vectors [$\mathrm{SL}(2,\mathbb{C})$ double cover of $\mathrm{SO}^+(1,3)$]. Is is possible to…
Mauricio
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votes
1 answer
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 author was talking about the Bloch sphere, it mentioned…
Joseph Stone
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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\sigma_i$.
The expectation values of Pauli matrices…
physicino
- 113
5
votes
1 answer
Lindblad operators seemingly not working as jump operators
I am currently trying to understand the Lindblad superoperator
$$\mathcal{L}[d]\rho = d \rho d^\dagger - (d^\dagger d \rho + \rho d^\dagger d)/2$$
for a simple 2 level system.
In the literature i found, the operator d is seen as a jump operator that…
David
- 53
5
votes
3 answers
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 we are studying a singlet (and we assume…
Euler
- 529
5
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1 answer
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 reflection preserving one coordinate and negating a…
actinidia
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5
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How to obtain $Y$ rotation with only $X$ and $Z$ rotation gates on the Bloch sphere?
Let's say you have a system with which you can perform arbitrary rotations around the $X$ and $Z$ axis. How would you then be able to use these rotations to obtain an arbitrary rotation around the $Y$ axis?
I have seen somewhere that rotation around…
PhysicsMan
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3 answers
Is is possible to generate circularly polarized light using a rotating half-wave plate?
Let's assume that I have a laser beam with a frequency $\omega$ that is linearly polarized (say coming out of a laser diode). If I pass it through a half-wave plate (HWP), the light that is transmitted will still be linearly polarized, although with…
QuantumExplorer
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4
votes
2 answers
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 electromagnetic wave over a certain amount of time, such…
Welcome_Green
- 479
4
votes
2 answers
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 seem to discuss the Bloch sphere!
I would…
Yuji
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How to calculate the bloch vector of a mixed state qubit
As I understand there are pure state and mixed state qubits. Pure states can be computed by
$$|\psi\rangle = \cos(\theta/2)|0\rangle + \exp(i \phi) \sin(\theta/2)|1\rangle . $$
Simple enough. You need the angles to find the point on the surface of…
Fitz
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