  We discuss three possible ways to address quantum physics behind chiral
magnetic effect and electric charge fluctuation patterns in heavy ion
collisions. The first one makes use of P-parity violation probed by local order
parameters, the second considers CME in quantum measurement theory framework
and the third way is to study P-odd * P-odd contributions to P-even
observables. In the latter approach relevant form-factor is extracted and
computed for weak magnetic field in confinement region and for free quarks in
strong field regime. It is shown that the effect is negligible in the former
case. We also discuss saturation effect - charge fluctuation asymmetry for free
fermions reaches constant value at asymptotically large fields.
