The Bloch Sphere is a useful geometrical representation of the state of a Qubit or any other two level quantum system. As discussed in this article an arbitrary pure state of a Qubit can be expressed in the computational basis as
where and are complex number such that . Since an overall phase has no observable effects, or can be chosen as real numbers and can written as
where and . The parameters and define a point on the sphere called the Bloch Sphere (Fig. 1).
The points in the surface of the sphere represent pure states of the qubit, with as the North pole and as the South pole, and the equator states of the form . Additionally any mixed state of a qubit can be represented as a point inside the sphere, with maximally mixed states at the center of the Bloch Sphere.
This representation is useful in Quantum Computation to visualize the effect of single qubit gates.
All text copyright © Marco Vinicio Sebastian Cerezo de la Roca.
The More You Know: Bloch Sphere por Marco Vinicio Sebastian Cerezo de la Roca se distribuye bajo una Licencia Creative Commons Atribución-NoComercial-CompartirIgual 4.0 Internacional.
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