  The effect of anisotropy for fluctuations of electric currents in magnetic
field is addressed within framework of quantum measurements theory. It is shown
that for free fermions in uniform magnetic field the anisotropy is of the same
sign as one expects for chiral magnetic effect and is related to triangle
anomaly. The corresponding decoherence functional contains anomalous
off-diagonal terms leading to correlation of fluctuations between observables
of opposite P-parity.
