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Unit vector
- A Bloch vector is a unit vector (cosphisintheta, sinphisintheta, costheta) used to represent points on a Bloch sphere.
mathworld.wolfram.com/BlochVector.html
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The Bloch sphere is a unit 2-sphere, with antipodal points corresponding to a pair of mutually orthogonal state vectors. The north and south poles of the Bloch sphere are typically chosen to correspond to the standard basis vectors and , respectively, which in turn might correspond e.g. to the spin -up and spin -down states of an electron.
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.
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...
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.
When we plot a pure state it will be a vector of length one (or if depicted as a dot it will appear on the surface of the Bloch sphere). When we plot a mixed state (or a bit from an entangled state) it will be a vector with length less than one (or the dot will appear on the inside of the sphere).
Jan 11, 2023 · A value of unity for the magnitude of the Bloch vector indicates a pure state. Calculate the eigenvalues of ρ and use them to calculate the entropy of the state represented by ρ.
