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Sensory systems are often tasked to analyse complex signals from the environment, separating relevant from irrelevant parts. This process of decomposing signals is challenging when a mixture of signals does not equal the sum of its parts, leading to an unpredictable corruption of signal patterns. In olfaction, nonlinear summation is prevalent at various stages of sensory processing. Here, we investigate how the olfactory system deals with binary mixtures of odours under different brain states by two-photon imaging of olfactory bulb (OB) output neurons. Unlike previous studies using anaesthetised animals, we found that mixture summation is more linear in the early phase of evoked responses in awake, head-fixed mice performing an odour detection task, due to dampened responses. Despite smaller and more variable responses, decoding analyses indicated that the data from behaving mice was well discriminable. Curiously, the time course of decoding accuracy did not correlate strictly with the linearity of summation. Further, a comparison with naïve mice indicated that learning to accurately perform the mixture detection task is not accompanied by more linear mixture summation. Finally, using a simulation, we demonstrate that, while saturating sublinearity tends to degrade the discriminability, the extent of the impairment may depend on other factors, including pattern decorrelation. Altogether, our results demonstrate that the mixture representation in the primary olfactory area is state-dependent, but the analytical perception may not strictly correlate with linearity in summation.