Questions tagged [bloch-sphere]

For questions related to the Bloch sphere. In quantum mechanics, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system (qubit), named after the physicist Felix Bloch. (Wikipedia)

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15
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5answers
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Can the Bloch sphere be generalized to two qubits?

The Bloch sphere is a nice visualization of single qubit states. Mathematically, it can be generalized to any number of qubits by means of a high-dimensional hypersphere. But such things are not easy ...
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2answers
293 views

Why is an entangled qubit shown at the origin of a Bloch sphere?

I'm unclear why the Bloch sphere representation of a maximally entangled qubit shows the state of the bit as being at the origin of the sphere. For example, this illustration shows the effect of ...
10
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2answers
465 views

Rotating about the y- or z-axis of the Bloch sphere

In order to rotate about an axis of the Bloch sphere we ususally use pulses e.g. in trapped ion quantum computing or superconducting qubits. Let's say we have rotation around the x-axis. What do I ...
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3answers
277 views

How to think about the Z gate in a Bloch sphere?

I am confused about how to understand the $Z$ gate in a Bloch sphere. Considering the matrix $Z = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$ it is understandable that $Z|0\rangle = |0\...
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4answers
790 views

Why do Bloch sphere wavefunctions have half angles?

Suppose we have a single qubit with state $| \psi \rangle = \alpha | 0 \rangle + \beta | 1 \rangle$. We know that $|\alpha|^2 + |\beta|^2 = 1$, so we can write $| \alpha | = \cos(\theta)$, $| \beta | ...
7
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2answers
202 views

From Q# measurements to Bloch sphere

I would like to represent the state of a qubit on a Bloch sphere from the measurements made with Q#. According the documentation, it is possible to measure a qubit in the different Pauli bases (...
7
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1answer
717 views

The general form of unitary operations on a single qubit

I want to understand the relation between the following two ways of deriving a (unitary) matrix that corresponds to the action of a gate on a single qubit: 1) HERE, in IBM's tutorial, they ...
6
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2answers
213 views

How to prove that Z operator rotates points on Bloch sphere about Z axis through 180°?

My idea was to apply $Z$ operator 𝐭𝐰𝐢𝐜𝐞, which leads us back to the point where we started from, and also show that after applying the $Z$ operator just 𝐨𝐧𝐜𝐞 we are not at the same point ...
6
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2answers
433 views

How to obtain Y rotation with only X and Z rotations gates?

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? ...
5
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2answers
233 views

Is there any online Bloch sphere simulator?

While writing this answer I realized it would be really helpful if I could show the OP a video or .gif of how qubit states in Bloch spheres transform under certain unitary operations. I googled up a ...
5
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1answer
109 views

Flying qubits compared with stationary qubits

In a previous question I asked how stationary bits could be processed by logic gates. I casually mentioned that I could visualize qubits traversing stationary logic gates, and @DaftWullie said “It ...
4
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1answer
40 views

How are measurements on $Z$ and $X$ axes interpreted in the Bloch sphere?

I'm having trouble understanding how the measurement on $z$ and $x$ axes can be interpreted in terms of the Bloch sphere representation. . I know that the state can be written as $$∣𝜓⟩=\cos(𝜃/2)|...
4
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2answers
301 views

Maximum number of “almost orthogonal” vectors one can embed in Hilbert space

In a Hilbert space of dimension $d$, how do I calculate the largest number $N(\epsilon, d)$ of vectors $\{V_i\}$ which satisfies the following properties. Here $\epsilon$ is small but finite compared ...
4
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1answer
86 views

Homeomorphism or stereographic projection corresponding to the set of mixed states within the Bloch sphere

The Bloch sphere is homeomorphic to the Riemann sphere, and there exists a stereographic projection $\Bbb S^2\to \Bbb C_\infty$. But this only holds for pure states. To quote Wikipedia: Quantum ...
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0answers
155 views

Computing Majorana “Stars”

I'm trying to implement Majorana's "stellar representation" of a spin-$j$ system as $2j$ points on the $2$-sphere in python. Consulting papers including Extremal quantum states and their Majorana ...
3
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3answers
108 views

How are orthogonal sets of pure states arranged in state space?

It is well known that the state of a (pure) qubit can be described as a point on a two-dimensional sphere, the so-called Bloch sphere. The mapping $\lvert\psi\rangle\mapsto \boldsymbol r_\psi$ that ...
3
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1answer
80 views

What utility is provided by the Bloch sphere visualization?

The Bloch sphere is a mainstay of introductions to quantum computing, but what utility does it actually provide? It can't usefully represent multiple qbits because of entanglement and requires a weird ...
3
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1answer
112 views

Drawing tangent vectors to the Bloch sphere with qutip

I need to plot drawings of qubit dynamics on the Bloch sphere. I know QuTip allows to do such drawings but I specifically need to represent evolution velocities on the Bloch sphere so I need to draw ...
3
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1answer
55 views

Plotting Bloch sphere in QuTiP

Is there anyone who reproduced the Bloch sphere given in the paper QuTiP: An open-source Python framework for the dynamics of open quantum systems by J. R. Johansson, P. D. Nation, Franco Nori? I am ...
3
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0answers
30 views

Spin precession using a laser

According to Christopher Monroe: "Modular Ion Trap Quantum Networks: Going Big", the hyperfine states of the valence electron in the Yb+ is used as a qubit. I know that we can change the spin ...
2
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1answer
169 views

What is the meaning of writing a state in its Bloch representation?

What is the meaning of writing a state $|\psi\rangle$ in its Bloch representation. Would I be correct in saying it's just writing out its Bloch vector?
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2answers
60 views

Why is the boundary of the set of states in the generalised Bloch representation comprised of singular matrices?

Consider an arbitrary qudit state $\rho$ over $d$ modes. Any such state can be represented as a point in $\mathbb R^{d^2-1}$ via the standard Bloch representation: $$\rho=\frac{1}{d}\left(\mathbb I +\...
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1answer
34 views

Bloch Sphere - Rotation Matrix

A qubit is given in the following form: $\left|\psi\right\rangle = \cos\left(\dfrac{\theta}{2}\right)\left|0\right\rangle + e^{i\phi}\sin\left(\dfrac{\theta}{2}\right)\left|1\right\rangle$. Let's ...
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0answers
35 views

How to add states on the Bloch sphere from a master equation?

Can you please help me to find an answer to this question: I am using qutip for the study of quantum systems. suppose I have calculated the solution of the master equation using the ...
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3answers
92 views

Purity of mixed states as a function of radial distance from origin of Bloch ball

@AHusain mentions here that the purity of a qubit state can be expressed as a function of the radius from the center of a Bloch sphere. The state corresponding to the origin is maximally mixed whereas ...
1
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1answer
136 views

What's a vector in the format of the Bloch Sphere?

The Bloch sphere isn't so intuitive for me. But I am not sure how you are supposed to manipulate it using vectors and matrices. How do you actually represent a vector on it? Is it $(\cos(a) , e^i\...
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1answer
19 views

How to prove that antipodal points on the Bloch sphere are orthogonal?

I started by assuming two antipodal states $$ |(\theta,\psi)\rangle=cos\dfrac{\theta}{2}|0\rangle+sin\dfrac{\theta}{2}e^{i\psi}|1\rangle\\ |(\theta+\pi,\psi+\pi)\rangle=cos\dfrac{\theta+\pi}{2}|0\...