# Questions tagged [bloch-sphere]

A geometrical representation of the pure state space of a two-level quantum mechanical system (qubit), used in quantum mechanics and computing.

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### How to write an arbitrary qubit density operator? [duplicate]

Physics noob here: I am reading the Wikipedia on Density Matrices (https://en.wikipedia.org/wiki/Density_matrix), and in the section labeled "Pure and mixed states", it states "An ...
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### Is there a nice formula to represent POVMs $\Pi$ in a Bloch-vector-like form?

A way to write a quantum state is to use the Bloch vector representation, i.e., $$\varrho = \frac{1}{2}\left(\mathbb{I}_2 + \boldsymbol{r} \cdot \boldsymbol{\sigma}\right)$$ In general a POVM for a ...
1 vote
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### 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 ...
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### What is the physical significance of phase difference in qubit or spin half? [duplicate]

Whenever it is talked about phase difference or lack of it, double slit example is used as the example. But I want to know what is the physical manifestation of phase difference for a qubit (or spin ...
1 vote
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### 90 degree rotation about $z$-axis on Bloch sphere

I am a beginner on quantum information and right now I study it from the lectures by Peter Shor. The lectures can be found on edX and can be viewed on YouTube as well. The lecture that I'm struggling ...
1 vote
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### Terminology for the symmetric vector product on the Bloch sphere

I was reading the paper "The extended Bloch representation of quantum mechanics and the hidden-measurement solution to the measurement problem" by Diederik Aerts, Massimiliano Sassoli de Bianchi. ...
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### Is there a geometrical representation of classical bits, like that of the Bloch Sphere for quantum bits?

Consider only a single qubit. We know that it can be accurately described using the so called Bloch Sphere. Is there a similar geometric construction used to describe classical bits?
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### Maximum number of "almost orthogonal" vectors one can embed in Hilbert space [closed]

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 ...
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### How to compute the axis of a rotation expressed as a combination of Pauli matrices? [closed]

An exercise asked to compute the axis and the angle of the rotation $THTH$. $(S.1)$ is easy to understand by using the identity $exp(i\theta A) = \cos(\theta) \mathbb1 + i \sin(\theta) A$ for $A$ s.t....
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### Constraints on higher-dimensional Bloch vectors

I'm interested in the constraints on the $(4^n-1)$-dimensional generalized Bloch vector (the Bloch vector for $n$ qubits). To the best of my knowledge, these are not analytically characterized for ...
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### How to transform coordinates of two-level system's eigenstates from spherical to momentum space?

In almost all references for some two-level quantum system (for example, this Wikipedia article), arbitrary eigenstates are defined in spherical coordinates, and can be written separately as follows (...