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--- wiki:bloch-sphere [August 13, 2026 at 18:55] – Ivan Janevski
+++ wiki:bloch-sphere [August 13, 2026 at 18:55] (current) – Ivan Janevski
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 **Bloch sphere** is a geometrical representation of a single qubit state as a point on the surface of a unit sphere in three-dimensional space. It provides an intuitive way to visualize qubit states and the effect of quantum gates as rotations. The Bloch sphere is named after physicist Felix Bloch.
-A single qubit $\lvert\psi\rangle = a\lvert 0\rangle + b\lvert 1\rangle$ has two complex probability amplitudes $a, b \in \mathbb{C}$, subject to the normalization constraint $|a|^2 + |b|^2 = 1$. Because global phase is physically unobservable, the qubit is fully described by just two real parameters: a polar angle $\theta \in [0, \pi]$ and an azimuthal angle $\varphi \in [0, 2\pi)$. We can therefore write any pure qubit state in the following standard form.
-$$\lvert\psi\rangle = \cos\frac{\theta}{2}\lvert 0\rangle + e^{i\varphi}\sin\frac{\theta}{2}\lvert 1\rangle$$
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+A single qubit $\lvert\psi\rangle = a\lvert 0\rangle + b\lvert 1\rangle$ has two complex probability amplitudes $a, b \in \mathbb{C}$, subject to the normalization constraint $|a|^2 + |b|^2 = 1$. Because global phase is physically unobservable, the qubit is fully described by just two real parameters: a polar angle $\theta \in [0, \pi]$ and an azimuthal angle $\varphi \in [0, 2\pi)$. We can therefore write any pure qubit state in the following standard form.
+$$\lvert\psi\rangle = \cos\frac{\theta}{2}\lvert 0\rangle + e^{i\varphi}\sin\frac{\theta}{2}\lvert 1\rangle$$