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The natural metric on the Bloch sphere is the Fubini–Study metric. The mapping from the unit 3-sphere in the two-dimensional state space to the Bloch sphere is the Hopf fibration, with each ray of spinors mapping to one point on the Bloch sphere.
Sep 4, 2015 · On the Bloch sphere, we can represent state with only 2 real parameters: the angles $\theta$ and $\phi$ But in the more explicit full full state vectors, there appear to be 2 complex numbers, and therefore 4 real numbers:
We call this sphere the Bloch sphere, and the unit vector \vec{s} defined by \theta and \varphi the Bloch vector. This is a very useful way to visualise quantum states of a single qubit and unitary operations that we perform on it.
Jul 6, 2018 · Bloch sphere is a physical representation of all possible qubit states. Each qubit is in its essence a vector on Bloch’s sphere. Each vector on the sphere can be represented in two basis: θ and ϕ. The first is θ which is the angle between the vector and the z-axis.
The natural metric on the Bloch sphere is the Fubini–Study metric. The mapping from the unit 3-sphere in the two-dimensional state space C2 to the Bloch sphere is the Hopf fibration, with each ray of spinors mapping to one point on the Bloch sphere.
Feb 7, 2021 · In this article, we’ll review in simple terms what exactly the Bloch sphere is, go over some basic but foundational math concepts, and then see how quantum states necessitate the use of a ...
The Bloch sphere is typically used in the quantum information context. So rather than talk about spin vectors, we’ll often be talking about the states of quantum bits.
