# 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 ...
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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 ...
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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 ...
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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 (...
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### Can all expectation values be constructed using only tensor products of local Pauli operators?

I understand that the Pauli operators and the identity matrix span the space of complex 2x2 matrices. Let's say you have two qubits and you can perform projective meausurements. So you can measure ...
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