CMB mode coupling with isotropic polarization rotation

We provide a new analysis technique to measure the effect of isotropic polarization rotation, induced by e.g. cosmic birefringence from axion-like particles and miscalibration CMB angle, via mode coupling in microwave background (CMB). Several secondary effects such as gravitational lensing optical-depth anisotropies lead observed anisotropies, i.e., non-zero off-diagonal elements covariance. To derive coupling, however, we usually assume no parity violation anisotropies. first contribution arising CMB. Since rotation leads then discuss use for constraining angle. find that constraints on angle measuring mode-coupling are comparable using $EB$ cross-power spectrum future high-sensitivity experiments CMB-S4 LiteBIRD. Thus, this can be used cross-check results obtained spectrum.