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We forecast how current ({\planck}) and future ({\prism}) cosmic microwavebackground (CMB) experiments constrain the adiabatic mode and its admixtureswith primordial isocurvature modes, using measurements of the reconstructed CMBlensing potential and lensing-induced CMB B-mode polarization anisotropies incombination with the CMB temperature and E-mode polarization anisotropies. Wefirst study the characteristic features of the CMB temperature, polarizationand lensing spectra for adiabatic and isocurvature modes. We then consider howlensing-induced B-mode polarization and lensing potential information canimprove constraints on an admixture of adiabatic and three correlatedisocurvature modes. We find that the CMB lensing spectrum improves constraintson isocurvature modes by at most 10% for the {\planck} and {\prism}experiments, with the limited improvement a result of the low amplitude ofisocurvature lensing spectra and cancellations between these spectra renderingthem only slightly detectable. There is a larger gain from using thelensing-induced CMB B-mode polarization spectrum, as measured by {\prism}, withconstraints on isocurvature mode amplitudes improving by as much as 40%relative to the CMB temperature and E-mode polarization constraints. Theaddition of both lensing and lensing-induced B-mode polarization informationconstrains isocurvature mode amplitudes at the few percent level or better,with percent level constraints or better possible in the case of admixtures ofthe adiabatic mode with one or two correlated isocurvature modes. Weinvestigate the dependence of our results to various assumptions in ouranalysis, such as the inclusion of dark energy parameters, the CMBtemperature-lensing correlation, and the presence of primordial tensor modes,and find that these assumptions do not significantly change our main results.

CMB lensing forecasts for constraining the primordial perturbations: adding to the CMB temperature and polarization information