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We show that the cosmic birefringence and miscalibrated polarisation anglescan be determined simultaneously by cosmic microwave background (CMB)experiments using the cross-correlation between $E$- and $B$-mode polarisationdata. This is possible because polarisation angles of the CMB are rotated byboth the cosmic birefringence and miscalibration effects,whereas those of theGalactic foreground emission only by the latter. Our method does not requireprior knowledge of the $E$- and $B$-mode power spectra of the foregroundemission, but uses only the knowledge of the CMB polarisation spectra.Specifically, we relate the observed $EB$ correlation to the difference betweenthe $\mathit{observed}$ $E$- and $B$-mode spectra in the sky, and use differentmultipole dependence of the CMB (given by theory) and foreground spectra (withno assumption) to derive the likelihood for the miscalibration angle $\alpha$and the birefringence angle $\beta$. We show that a future satellite missionsimilar to LiteBIRD can determine $\beta$ with a precision of ten arcminutes.

Simultaneous determination of the cosmic birefringence and miscalibrated polarisation angles from CMB experiments