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How are antipodal points chosen in the Bloch sphere?
This is the Bloch sphere, also known to mathematicians as the Riemann sphere . 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
What are the pure states of the Bloch sphere?
It is usually said that the points on the surface of the Bloch sphere represent the pure states of a single 2-level quantum system. A pure state being of the form: $$ |\\psiangle = a |0angle+b |1\\
Which is the mapping from the unit 3-sphere to the Bloch sphere?
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. , where the coefficient of (or contribution from) each of the two basis vectors is a complex number. This means that the state is described by four real numbers.
Why is the Bloch sphere named after Felix Bloch?
Bloch sphere. In quantum mechanics, 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. Quantum mechanics is mathematically formulated in Hilbert space or projective Hilbert space.
Which is the stereographic projection of the Bloch sphere?
Call this point P. Point u on the plane z = 0 is the stereographic projection of point P on the Bloch sphere. The vector with tail at the origin and tip at P is the direction in 3-D space corresponding to the spinor . The coordinates of P are
What kind of vector is the Bloch sphere?
is called the Bloch vector . It is this vector that indicates the point within the sphere that corresponds to a given mixed state. Specifically, as a basic feature of the Pauli vector, the eigenvalues of ρ are . Density operators must be positive-semidefinite, so it follows that
Why are the north and south poles of the Bloch sphere chosen?
The north and south poles of the Bloch sphere are typically chosen to correspond to the standard basis vectors , respectively, which in turn might correspond e.g. to the spin -up and spin -down states of an electron. This choice is arbitrary, however.