 To construct a counterexample for 2-dimensional Hilbert space, known as a qubit, let the hidden variable be a unit vector formula_23 in 3-dimensional Euclidean space.Using the Bloch sphere, each possible measurement on a qubit can be represented as a pair of antipodal points on the unit sphere.Defining the probability of a measurement outcome to be 1 if the point representing that outcome lies in the same hemisphere as formula_23 and 0 otherwise yields an assignment of probabilities to measurement outcomes that obeys Gleason's assumptions.