Poincaré Sphere
Poincaré sphere may refer to: * Poincaré sphere (optics), a graphical tool for visualizing different types of polarized light ** Bloch sphere, a related tool for representing states of a two-level quantum mechanical system * Poincaré homology sphere Poincaré is a French surname. Notable people with the surname include: * Henri Poincaré (1854–1912), French physicist, mathematician and philosopher of science * Henriette Poincaré (1858-1943), wife of Prime Minister Raymond Poincaré * Luci ...

Poincaré Sphere (optics)
Polarization ( also polarisation) is a property applying to transverse waves that specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. A simple example of a polarized transverse wave is vibrations traveling along a taut string ''(see image)''; for example, in a musical instrument like a guitar string. Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string. In contrast, in longitudinal waves, such as sound waves in a liquid or gas, the displacement of the particles in the oscillation is always in the direction of propagation, so these waves do not exhibit polarization. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves, gravitational waves, and transverse sound waves (shear waves) in solids. An electromagnetic ...
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Bloch Sphere
In quantum quantum mechanics, mechanics and Quantum computing, computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level system, two-level quantum mechanical system (qubit), named after the physicist Felix Bloch. Quantum mechanics is mathematically formulated in Hilbert space or projective Hilbert space. The pure states of a quantum system correspond to the one-dimensional subspaces of the corresponding Hilbert space (and the "points" of the projective Hilbert space). For a two-dimensional Hilbert space, the space of all such states is the complex projective line \mathbb^1. This is the Bloch sphere, which can be mapped to the Riemann sphere. The Bloch sphere is a unit N-sphere, 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 , 0\rangle and , 1\rangle, respectively, which in turn migh ...
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