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Unit 2-sphere
- The Bloch sphere is a unit 2-sphere, with antipodal points corresponding to a pair of mutually orthogonal state vectors.
en.wikipedia.org/wiki/Bloch_sphere
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In quantum mechanics and computing, 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. [1] Mathematically each quantum mechanical system is associated with a separable complex Hilbert space .
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.
Feb 7, 2021 · Put in a sentence, the Bloch sphere is a geometric representation of the aforementioned “quantum states” on the surface of a 3d unit sphere, which helps researchers understand the data of...
Sep 4, 2015 · One common way to represent a state in the Bloch sphere is to give just the two $\theta$ and $\phi$ angles as shown below: Source. Since a sphere is non-Euclidean, a good way to visualize it is to walk through some easy to understand paths around it. On the following image we do two paths: start at 0, pass through +, 1, -, and return back to 0
5 days ago · The qubit |psi>=a|0>+b|1> can be represented as a point (theta,phi) on a unit sphere called the Bloch sphere. Define the angles theta and phi by letting a=cos (theta/2) and b=e^ (iphi)sin (theta/2). Here, a is taken to be real, which can always be made real by multiplying |psi> by an overall phase factor (that is unobservable).
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 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.
