Abstract
A group is an algebraic structure equipped with binary associative multiplication, identity element and inverse operation with respect to identity. Lie group is a smooth manifold with group multiplication and the inverse being smooth functions. Therefore as one chooses manifold coordinate charts, various parametrizations of multiplication and inverse operations arise. Recently, the simple probability representation of qubit states and observables and an associated triangle geometrical picture called ‘quantum suprematism’ were introduced. At its core lies the representation of the Bloch sphere by correlated dichotomic probability distribution. The aim of the present paper is the introduction of probability parametrization of two classical compact and non-compact Lie groups, SU(2) and SU(1,1) respectively.
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