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How to understand Bloch sphere?
The Bloch Sphere is is a generalisation of the representation of a complex number z with |z|2 = 1 as a point on the unit circle in the complex plane. and x2 + y2 = 1 is the equation of a circle of radius one, centered on the origin.
Why Bloch sphere?
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 the given superposition of a quantum state in a nice, mathematically sound way.
Who invented the Bloch sphere?
Henri Poincaré
Indeed Henri Poincaré was the first to suggest the use of this kind of geometrical representation at the end of 19th century, as a three-dimensional representation of Stokes parameters.
Who invented Bloch sphere?
physicist Felix Bloch
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. Quantum mechanics is mathematically formulated in Hilbert space or projective Hilbert space.
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
The Bloch sphere parametrizes not only pure states but mixed states for 2-level systems. The density operator describing the mixed-state of a 2-level quantum system (qubit) corresponds to a point inside the Bloch sphere with the following coordinates: are the coordinates of the individual states (on the surface of Bloch sphere).
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
Can a Bloch sphere be generalized to a quantum system?
The Bloch sphere may be generalized to an n-level quantum system, but then the visualization is less useful. For historical reasons, in optics the Bloch sphere is also known as the Poincaré sphere and specifically represents different types of polarizations.