# Qutrit States as Probability Vectors

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A particle with spin can represent a qutrit. Any qutrit state can be associated with a 15-dimensional probability vector whose components have definite physical meaning. The discrete variable is the spin projection and defines a direction of spin projection measurement, . The ends of the vectors lie on the unit 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 14-simplex. If the directions are chosen with equal probability, then for all . In that case, the vectors can be labeled by 10 real non-negative numbers , . To illustrate such a probability vector we fix seven components, namely , , and , , that is, we determine a hyperplane that intersects the simplex, with the cut set depending on three real non-negative parameters , , and . The cut set is nothing else but a cube , . In other words, any qutrit state is associated with the 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

## Snapshots

## Details

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

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

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