For rotationally symmetric quantum channels, spin polarization can be inverted by at most a factor of -j/(j+1) and amplified into a larger spin by at most (j_B+1)/(j_A+1), with conservation-law deviation bounded by channel unitarity.
In this case the unitarity is given by u(E) = 1 3 ( 4p0(E)2 + 4 3(1−p0(E))2− 1 ) , (165) and the deviation by ∆(E) = 4 9 (1−p0(E))2
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Robustness of Noether's principle: Maximal disconnects between conservation laws and symmetries in quantum theory
For rotationally symmetric quantum channels, spin polarization can be inverted by at most a factor of -j/(j+1) and amplified into a larger spin by at most (j_B+1)/(j_A+1), with conservation-law deviation bounded by channel unitarity.