# Representation of Qubit States by Probability Vectors

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Any qubit state is associated with a six-dimensional probability vector with components , where is the spin projection and defines a direction of spin projection measurement, . The ends of the vectors are on the sphere which is illustrated in the top-left corner. In general, is a probability distribution function of two discrete variables and , and determines a point on the five-simplex. If the directions are chosen with equal probability, then for all . In that case, a one-to-one correspondence can be established between all probability vectors and all points inside a cube , , which is illustrated in the top-right corner. In other words, any quantum state is associated with a probability vector of the form

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Contributed by: Sergey Filippov and Vladimir I. Man'ko (February 2010)

Based on a program by: S. M. Blinder

Open content licensed under CC BY-NC-SA

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## Details

Representation of spin states by finite dimensional probability vectors is considered in

S. Filippov and V. Man'ko, arXiv, "Inverse Spin-s Portrait and Representation of Qudit States by Single Probability Vectors," 2010.

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