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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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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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2answers
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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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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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1answer
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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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4answers
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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 | ...
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0answers
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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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1answer
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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 ...
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2answers
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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 (...
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2answers
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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 ...
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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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3answers
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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\...