# 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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### Affine Map of the Bloch sphere

I am referring to Equation (8.89) to (8.92) in Chapter 8 of "Quantum Computing and Information 10th Anniversary Edition" by Nielsen and Chuang. This section deals with the geometric picture of single ...
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### What is the probability of a single qubit state lying over the surface of Bloch sphere?

I want to compute the POVM $E_{(\theta, \phi)}$ of the measure which gives the probability of a qubit state lying over the surface of Bloch sphere, with angles $\theta, \phi$. How can I handle this? ...
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### Can a qubit be in the inside of the Bloch Sphere?

Can qubit be inside Bloch Sphere, i.e. its length is less than 1? If yes, how we represent that state since we have only parameter for angles and not the length (norm) of the vector?
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### 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 ...
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### How can I find the $\theta$ and $\phi$ values of a qubit on the Bloch sphere?

If I have the following state: $$\left| \varphi \right>=\frac{1}{\sqrt{2}}\left(\left(\frac{1+i}{\sqrt{2}} \right)\left| 0 \right> + \left| 1\right>\right)$$ How can I find the $\theta$ ...
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### Find coordinates $\theta$ and $\phi$ on the Bloch sphere of a given qubit state [duplicate]

In last time there is a lot of questions how to find $\theta$ and $\phi$ for particular state on Bloch sphere. I think that it would be useful to solve one example to stop stream of very similar ...
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### 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 ...
325 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 ...
251 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 ...
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### 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 ...
189 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 ...
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### 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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### 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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### 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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### 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 ...
290 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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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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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### 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? ...
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### 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 ...
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### 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 ...
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### 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 ...
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 ...
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\...