Fig. 2

The Bloch sphere representation of the measurement situation. a The state \(\left| \psi \right\rangle\) of the polarized photon is represented by \(\hat v\), while the projectors Q(0) and Q(θ) correspond to unit vectors \(\hat n\) and \(\hat n_\theta\), respectively, and m is give by m = \(\left( {1 - p} \right)\hat n + p\,\hat n_\theta\). The bound on the probability of transmission ξ(θ, p) is obtained from the vector m, ξ(θ, p) = \({\textstyle{{1 + \left| m \right|} \over 2}}\). The uncertainty relation defined by the probability of transmission (P(transmission) ≤ ξ(θ, p) < 1) is saturated by the \(\left| \psi \right\rangle\) with Bloch vector \(\hat v\) parallel to m. b The situation when Alice tries to steer to the least uncertain state. It is achieved only when \(\hat v{\mathrm{||}}m\)