We present a state-of-the-art calculation of the next-to-leading-order electroweak corrections to ZZ production, including the leptonic decays of the Z bosons into $mu^+mu^-mathrm{e}^+mathrm{e}^-$ or $mu^+mu^-mu^+mu^-$ final states. We use complete leading-order and next-to-leading-order matrix elements for four-lepton production, including contributions of virtual photons and all off-shell effects of Z bosons, where the finite Z-boson width is taken into account using the complex-mass scheme. The matrix elements are implemented into Monte Carlo programs allowing for the evaluation of arbitrary differential distributions. We present integrated and differential cross sections for the LHC at 13 TeV both for an inclusive setup where only lepton identification cuts are applied, and for a setup motivated by Higgs-boson analyses in the four-lepton decay channel. The electroweak corrections are divided into photonic and purely weak contributions. The former show the well-known pronounced tails near kinematical thresholds and resonances; the latter are generically at the level of $sim-5%$ and reach several $-10%$ in the high-energy tails of distributions. Comparing the results for $mu^+mu^-mathrm{e}^+mathrm{e}^-$ and $mu^+mu^-mu^+mu^-$ final states, we find significant differences mainly in distributions that are sensitive to the $mu^+mu^-$ pairing in the $mu^+mu^-mu^+mu^-$ final state. Differences between $mu^+mu^-mathrm{e}^+mathrm{e}^-$ and $mu^+mu^-mu^+mu^-$ channels due to interferences of equal-flavour leptons in the final state can reach up to $10%$ in off-shell-sensitive regions. Contributions induced by incoming photons, i.e. photon-photon and quark-photon channels, are included, but turn out to be phenomenologically unimportant.
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